Roxana García sat in a packed classroom on a recent night in Jackson Heights, Queens, with 38 strangers — a chef, an I.T. technician, and a business manager among them — all with a single goal: To get a job in construction, one of the few industries open to New York’s surging migrant population.

Ms. García, 36, a nurse who flew to New York three months ago from Guayaquil, Ecuador, with her partner and two children, has subsisted since then on housecleaning jobs, but in construction, she sees a future: being able to afford better care for her prediabetic teenager and the means to take her family to Disneyland.

“I came here with a suitcase full of dreams,” she said in Spanish. “If I can make this into a career, that would be excellent, because I can’t focus on what I once was.”

Attracted by the prospect of steadier work and better pay, more migrant women are entering the male-dominated construction industry, social service providers said, at a time when the city is struggling to accommodate tens of thousands of asylum seekers.

They face sexism from co-workers and employers, exploitative labor practices, and dangerous conditions on the job. But for newcomers who may not qualify for legal residency for years, if ever, it can also be the first rung on the ladder to a better life.

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