The recent influx of migrants crossing the southern border has been one of the biggest in American history. Many were turned back, but more have been allowed to stay and fight deportation in court. Thousands have headed to New York City to try their luck.

Todd Heisler/The New York Times

Each of the five followed a different path, but they are all trying to create a life here, and they all worry about the likelihood that, eventually, they could be ordered to leave.

We wanted to understand what might happen to them next.

The people we spoke with were all given notices to appear in immigration court when they crossed the border, and they are at various stages of the deportation process, which can take years. The Biden administration has given temporary protection from deportation to people from places like Venezuela and Ukraine, where conditions have been deemed too dangerous for migrants to return.

Some have applied for asylum, but it can take many months to submit an application, and migrants are not allowed to apply for a work permit until 150 days later. Many spend their first months or years in New York in limbo, unable to work legally, waiting for hearings and permits, often in uncertain living situations.

Step 1: Finding shelter

When they arrive in New York, many migrants have little money, and many opt to stay in one of the city’s homeless shelters. Nearly 140,000 migrants have checked into the city’s intake system in the last year and a half; about half that number are living in shelters today.

The city, strained past its breaking point, is now forcing shelter residents to reapply after certain time limits (30 days for single adults; 60 for families). Migrants say the rules are making it hard to hold jobs and could cause them to miss important mail about their immigration cases.

Milton Vargas was one of four people we spoke with who were placed in shelters.

After arriving in New York last year, along with his pregnant wife and four children, they traveled to an intake center for homeless families in the Bronx. After waiting there for nine hours, they were sent to a hotel near Central Park.

There, they rested for 36 hours. “I didn’t want to interrupt my seven-month-pregnant wife’s rest, and we didn’t go out,” Mr. Vargas said. Eventually they learned about a nearby church where they could get clean clothes donated by neighbors. “Little by little we understood how to navigate the neighborhood,” Mr. Vargas said.

After Eduardo Gómez arrived in New York last year, a friend picked him up from the Port Authority Bus Terminal and took him to Randall’s Island, where the city had set up an 84,400-square-foot tent to house migrants.

He lived in four different shelters over the course of nearly a year. Then, he was asked to leave. “The people in the government wanted us to leave the shelter, but they did not understand all the confusion we were experiencing,” he said. “It is not an easy system to navigate.”

He paid $450 to sleep on a couch in an apartment in Williamsburg, Brooklyn, for a month. Then, he and a friend found a mobile home in Queens, which they now rent for $1,200 per month.

When Gaoussou Ouattara arrived at Kennedy Airport in August, he was unable to reach anyone at the organization that had flown him to New York. He took a taxi to Manhattan and tried again to get in touch with the nonprofit, with no luck. That night, he slept on the street. The next day, he contacted people he had met on his journey to the United States, who told him to go to the Roosevelt Hotel, where he went through the city’s intake process and was placed in a shelter in Harlem.

Manuel Rodríguez had left the few belongings he had in Mexico, and arrived in New York in March with only the clothes he was wearing. His sister’s husband picked him up from Kennedy Airport.

They went to Flushing, Queens, and his brother-in-law lent him $200 to buy new clothes: underwear, socks, pants, T-shirts and a sweatshirt. “Only the essentials, because I have nothing,” he said. They ate that day in Flushing and then went back to a room his brother-in-law was renting in Whitestone, Queens, for $1,000 per month, where he had invited Mr. Rodríguez to stay.

Step 2: Earning money

For most migrants, the waiting period for a legal work permit is long, sometimes years. During those long waiting periods, many try to find ways to support themselves.

Eduardo Gómez was one of four people we spoke with who found odd jobs that pay cash.

When he arrived in New York last year, he quickly started looking for a way to earn money. He had worked as an electronics technician repairing cell phones in Venezuela and eventually found a job installing security cameras, but it lasted only 15 days. “Everyone asked me for papers and I didn’t even know what they were talking about,” he said.

In early 2023, Mr. Gómez learned he may qualify for asylum, but he needed money for a lawyer. He paid a staffing agency in Queens $150 and was sent to a job at a food packaging company in Flushing. He was paid $540 a week for 60 hours of work.

“I lasted two weeks there because they exploited me a lot and I just wanted the money to buy a motorcycle to start delivering food,” Mr. Gómez said.

After Jorda Colomer and her family were placed in a shelter last year, they found a church that provided them with clean clothes, and she and her husband enrolled their son in school. Then they set out to look for jobs. They left cover letters at businesses in Hell’s Kitchen, the Upper West Side, Midtown, Queens and Brooklyn.

Finally, Ms. Colomer met a man at another church who paid her $20 to clean his home for five hours, she said. “Everyone told me that he was exploiting me, but I had nothing and $20 was something, and he gave me food,” Ms. Colomer said. “A month later he raised it to $40 per day.”

She quit to take care of her children, and eventually her husband, Floyd, found a job cleaning a supermarket in the Bronx.

Gaoussou Ouattara volunteers to help other migrants. He uses his language skills to help people sign up for IDNYC cards, and to welcome migrants who arrive on buses at the Port Authority. The work is nonstop, he said. He often wakes up at 3 a.m. to go to the Port Authority, and sometimes spends more than 12 hours a day meeting new arrivals and directing them to the Roosevelt Hotel to be placed in a shelter.

“There’s no salary,” he said, adding: “In fact, I need a work permit to be able to work. Maybe with that, I’ll get a good job somewhere, that can pay me? Even if it’s at 15 dollars — I don’t know how much, at 20 dollars — I could have a home, take care of myself and then continue to help them.”

Step 3: Avoiding deportation

For most migrants, the only path to staying in the United States legally is winning asylum.

It is not a straightforward process. Asylum applications are more than 10 pages long, must be filled out in English, and require extensive information and documentation, all of which must match eventual testimony at a hearing. “This is one of the most complicated applications in immigration law and is extremely time consuming,” reads a guide created by the Legal Aid Society.

Most migrants need substantial help from lawyers to compile an application and succeed in subsequent hearings. In recent years, courts in the United States have denied asylum to most applicants.

Manuel Rodríguez was one of four people we spoke with who has submitted an asylum application.

In September, he submitted his application with help from a lawyer he found in Queens, who charged $3,000. Mr. Rodríguez has so far paid the lawyer $1,500, and agreed to pay the rest if he is granted asylum. Because he is from Venezuela, Mr. Rodríguez is eligible for the temporary protection offered by the Biden administration, but he doesn’t know if he will apply, because he is worried that it will be as expensive as the asylum process.

Eduardo Gómez met a paralegal at a church event for migrants in early 2023, who suggested he find a lawyer and apply for asylum. A friend recommended a lawyer in California, whom he met on a video call. The lawyer agreed to help submit his asylum application for $2,500. In March 2023, his application was submitted after he paid the lawyer $1,000, and agreed to pay the rest over time. He is waiting to hear from the lawyer about his court date, but he now has a work permit and, in February, started working as a delivery driver.

Gaoussou Ouattara does not believe he can afford a lawyer who would help him through the entire asylum process, beyond submitting the application. Much of what he knows about the process he learned from speaking to other migrants. He has heard that lawyers who provide full representation can cost $5,000 to $7,000, and that free lawyers are hard to find.

Milton Vargas and Jorda Colomer submitted applications with help from a nonprofit organization, Project Rousseau, which provides free representation for children and families.

“Both Milton and Jorda have a wait that will be many years long,” said Andrew Heinrich, the lawyer at Project Rousseau who is representing Mr. Vargas and Ms. Colomer.

“Someone arriving in New York today should have the same expectations,” he said.