The call came at 6:30 a.m. on Feb. 24, just hours after Russia invaded Ukraine. It threw a lifeline to the Trushchenkov family. "Come, my apartment is yours from the beginning of next month," said a friend, phoning from 230 miles away in Warsaw to offer a good deal on a sublet. So began the journey that brought 11 Trushchenkovs-six adults and five children-from across Ukraine to a cramped ground floor apartment in the Polish capital. "We only had room for toothbrushes and some gold," says Olga, a 38-year-old mother of two, recalling her four grueling days of travel.

In Poland, the Trushchenkovs relied on a country's kindness. Deliveries of secondhand clothing arrived on their doorstep. They collected 500 zloty ($108) per child each month from the government. But their rent was 6,000 zloty, and they'd spent most of their cash during the escape. "All our savings went like water in the first few days as we had to pay for hotels and fuel," says Zoia, the family's 67-year-old matriarch. They needed jobs, fast.

Whether families like the Trushchenkovs find jobs, return home, or move on carries enormous stakes for Poland. It rose out of communist-era poverty to achieve one of the highest living standards in Eastern Europe. Today the country has a labor shortage and an aging population. Its jobless rate in May was only 2.7%, the second-lowest in the European Union after the Czech Republic.

As cruel as it is, the war in Ukraine could turbocharge Poland's $670 billion economy. The country is accommodating more than 2 million refugees, an astonishing number for a nation of 38 million. It's as if the entire city of Houston suddenly pulled up stakes and drove to California. In the first weeks of the war, the population of Warsaw alone swelled by more than 15%. And Poland's government, as well as its employers, want as many people as possible to stay for good. The newcomers have sought-after skills. Among the Trushchenkovs, Olga teaches English, her mother is a retired doctor, and her niece is an accountant.

But Poland is more expensive than Ukraine; even before the war, Poland was short about 2 million apartments, according to Warsaw-based Heritage Real Estate's think tank. Rents have risen 20% since. At Warsaw's central railway station, signs in English and Ukrainian warn refugees that Poland's biggest cities are overcrowded and say that they have a better chance of finding jobs and homes in smaller towns. Schools are overwhelmed. And there's a language barrier; although Ukrainian can be used in casual conversation with Polish speakers, Polish is necessary in the workplace. "I was initially like a dog-only understood, couldn't speak," Olga says of her Polish.

Then and now, space and money are tight for the Trushchenkovs-a great-grandmother sleeps on a couch in the living room-but the family knows how lucky they are. "It's a luxury compared to people who have to live together at refugee centers set up in exhibition halls," Zoia says. "We have a roof over our heads."

Still, they're torn about the future. Poland's gain is Ukraine's loss. Their home country's economy is likely to decline by at least 40% this year and won't rebound until the refugees return, according to Oleg Ustenko, an adviser to Ukraine's president. Zoia's husband, Volodymyr, remembers the family's 48-hour wait at the border crossing in Ukraine's Zosin-Ustyluh. Images haunt him: women with children, bags and backpacks in tow, trudging through rain and snow. "For me it felt like the future of Ukraine was leaving," he says.

In relief kitchens, hostels, clinics, and welfare offices, Polish society is sparing no expense to make Ukrainians feel welcome. In the war's first three months, private citizens spent as much as $2.1 billion on aid, the Polish Economic Institute estimates, and the government has pledged $3.4 billion for this year. More than 1.2 million Ukrainians have been granted social security numbers, giving them access to health care, education, and social benefits.

In July the government launched a website in Polish, Ukrainian, and English for refugees seeking jobs. Schools are offering Polish classes; nongovernmental agencies are providing day care so parents with young children can work. By late July, 385,000 Ukrainian refugees had found jobs since arriving in Poland, according to the labor ministry.

Researchers and business groups estimate that 20% to 50% of the Ukrainian refugees could remain after the war. That would amount to as many as 1 million people, equal to the number of Ukrainians who resettled in Poland in the eight years before the war. Pawel Dobrowolski, chief economist at the Polish Development Fund, calls the influx a "large positive supply shock." He says migrants, mainly from Ukraine, have helped keep Poland's economy growing at one of the fastest rates in Europe over the past few years. In the first quarter, gross domestic product rose 8.5% compared with the year before.

Businesses are hanging help wanted signs. Austrian construction company Strabag estimates the industry needs 100,000 workers in Poland. "We hope that most of the refugees who have reached our country will stay here," says Wojciech Trojanowski, CEO of its Polish business. His company has granted paid leave to several dozen of his Ukrainian workers who've gone back home to fight in the war. He expects them to return.

The professions are hiring, too. In the city of Lodz, 80 miles west of Warsaw, BZB Projekt, a construction design studio, now counts three Ukrainian women-two architects and one accountant-among its staff of 45. "Business has a role to play in building bridges where no one else can," says Bartlomiej Zgorzelski, who runs the firm. JPMorgan Chase plans to hire as many as 50 refugees in Warsaw for positions in finance, human resources, and operations. It will also help them find housing and preschool child care. Competition is fierce; 1,400 people applied.

"If we really want Ukrainians to stay, we need to try harder to help them make their life here," says Anna Rulkiewicz, CEO of Lux Med, a network of health clinics owned by U.K.-based health-care company Bupa. "Ukrainian refugees could be a godsend for Poland, given the country's demographic challenges."

To ease the housing crunch, corporations are donating hotel rooms and buildings. German industrial company Siemens has converted 28,000 square feet of Warsaw office space into a shelter for 160 Ukrainians. In July, Volodymyr and Zoia got a temporary respite from their multigenerational apartment, courtesy of the city of Warsaw. It's paying for them to stay for three months in a three-star hotel, a temporary home for 200 Ukrainians. "We haven't slept so well in ages," Volodymyr says.

In one way, the outpouring of support seems surprising. Poland's right-wing nativist government has long been among the most anti-immigrant in Europe. It refused to accept any asylum seekers during the continent's 2015 migrant crisis. And as it threw the door open to Ukrainians, the government built a 116-mile border wall with Belarus, ostensibly to prevent illegal crossings of refugees from the Middle East. Some relief groups have complained of racism; the welcomed Ukrainians are White and Christian, while the excluded Middle Eastern refugees are Brown and Muslim. No doubt, the Ukrainians benefit from familiarity and a distrust of Moscow shared by the Poles. A sizable Ukrainian diaspora settled in Poland after Russia annexed Crimea and stoked the conflict in eastern Ukraine in 2014.

The war is also changing attitudes toward immigrants. The latest Pew Research Center survey, conducted from March 25 to May 5, showed that 8 in 10 Poles now support taking refugees from countries where people are fleeing violence and war, up from 49% in 2018. There are signs everywhere that Poland is adapting to the newcomers. "We Speak Ukrainian" signs in Cyrillic have sprung up in stores. ATMs and self-checkouts in supermarkets display instructions in the neighboring country's language.

On the aptly named Ulica Kijowska-Kyiv Street-a new restaurant serves the Ukrainian version of steaming pierogi (stuffed dumplings) and bowls of deep-maroon borscht (beet soup). It's a provisional place, a pop-up; bathed in the scent of frying onions, customers dine under white ventilation pipes on the ceiling. Posters show ears of wheat, Ukraine's best-known export. One afternoon, Natalia Hipska, a former kindergarten administrator who fled Ukraine with her 12-year-old son, assembles dumplings of dough and minced meat, dropping them into pans of boiling water. "Where we come from, there are rockets flying, so we're not planning to go back," says Hipska, who lives in a free hostel with no hot water. "I have a job and just one son, so I can work. I'd like to find an apartment, at least in communal housing."

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For the sprawling Trushchenkov clan, however, the decisions are far more complex.

Before the war, Volodymyr and Zoia Trushchenkov lived in a four-room bungalow with a garden in Ratne, a small town in northwest Ukraine. It was the house where Zoia grew up; her mother still lived there with the couple. Zoia had retired as an emergency room physician, but Volodymyr still worked, selling spare parts for a German agricultural machinery company. "Even though I have traveled the world, I always missed my home," Volodymyr says.

The couple have three adult daughters. Two lived in Irpin, a suburb of Kyiv, in a complex of modern high-rise buildings with manicured hedges and fountains. Ukrainian officials say Russian soldiers targeted civilians, committing atrocities in the town. The apartment where their daughter Olga lived with her family is now little more than a shell with a hole where the bathroom used to be.

In Warsaw, Olga, mother of a 12-year-old and a 4-year-old, was the first to find a job. In Irpin, she'd taught English. Two weeks after arriving, while her husband stayed in Ukraine to fight, she became a teaching assistant in a primary school, where she helped Ukrainian students integrate into classes. She expects to start teaching English full time when the school year starts in September.

Not long after, her mother found work thanks to her medical training. Lux Med, the health-clinic operator, was hiring. A thousand Ukrainian doctors and nurses applied for 150 positions. Two days after seeing an online posting, Zoia got a job at one of the company's Warsaw centers, which serves 200 Ukrainian refugees a day for free. Her contract runs until the end of September.

One afternoon in July, Zoia strolls through the halls of a Lux Med clinic on the second floor of a Marriott hotel across from Warsaw's central train station. She wears a white coat, a ribbon in the colors of the Ukrainian flag clipped to her name tag. She translates for Ukrainian patients, helping them fill out questionnaires and set up appointments.

Here she is in her late 60s, after a lifetime of training, starting over as a medical assistant. She hopes that once her Ukrainian credentials come through, she can come out of retirement to do what she loves-saving lives as an ER physician. Lux Med is helping doctors navigate the red tape of obtaining a license to practice medicine. For all of Poland's assistance, Zoia sees evidence of Ukrainians heading elsewhere. She's helping many get medical exams for visa applications to the US or Canada.

Her own family is unsettled, too. Back in the Ukrainian city of Lutsk, Oksana Drahan, her 38-year-old niece, used to work as an accountant. But she hasn't found a steady job in Warsaw because she doesn't speak Polish. With two small children, she gets by on income from cleaning houses, making dolls, and crocheting clothing to sell online.

Zoia's daughter, Tetiana, 46, who has an 18-year-old son, is thinking about moving to Italy. There she'd reunite with her other sister, Irina, who's been living in Bologna with five children and her Italian husband. Zoia wants to keep the family together and points out that the labor market isn't as strong in Italy. "We're staying here," she says. "At least for the time being, then we'll see."

Zoia's husband also struggled to find work. Volodymyr lasted just four hours in his first job, installing insulation on pipes in buildings. It was too physically demanding for a man of 67. He then applied to be a courier with the DHL delivery service but didn't know Warsaw well enough to navigate the streets. Four weeks after his arrival and still jobless, he was beginning to lose hope. Searching the web, he stumbled onto a job that piqued his interest, helping refugees at the Warsaw Family Assistance Center, a four-story building downtown that houses 132 Ukrainians.

Late one Monday morning, like a greeter at Walmart, he wears a blue vest over his checked shirt and pitches in where he can. He helps a couple who lost their social security number. He takes an émigré in a wheelchair to a nearby ATM. He serves lunches to hungry families. "I found the type of job I couldn't have dreamt of at my age," says Volodymyr, who's also the center's handyman. "I can interact with other people, and I speak Polish, English, Russian, Ukrainian, and some Italian, so I can help them, which is really rewarding."

None of the family members wants to reveal exactly how much money they're making in their jobs. Volodymyr will only say that he and his wife are earning more than they did in Ukraine, though it's still tough to make ends meet.

There have been moments of joy. In March, a week after arriving in Poland, their seven relatives living in Italy came to visit for a special occasion: Zoia's mother's 91st birthday. Four generations gathered to toast her with Champagne.

Two months later, Zoia and seven members of her family used free railway tickets for refugees to travel to Gdansk and Sopot, two resort towns on the Baltic Sea. On a sunny weekend they met old friends from Kyiv, a urologist and his family, who'd fled to the western Polish city of Wroclaw. Sadly for Zoia and her husband, they've since returned to Ukraine. On that day, their children seemed to be enjoying Poland. They braved the freezing water to frolic in the surf.

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Skolimowski is Bloomberg's Warsaw bureau chief. Bloomberg's Andrea Dudik, Konrad Krasuski, Aliaksandr Kudrytski, and Olesia Safronova contributed to this report.