Pursuit, by design, seeks people with the “highest need” and potential, but it is selective, accepting only 10 percent of its applicants. Its outreach relies heavily on presentations at public housing buildings and libraries, and word-of-mouth referrals.

The program is free for the participants, who can attend either weekdays or on evenings and weekends. No previous coding experience is required.

Max Rosado heard about the Pursuit program from a friend. Intrigued, he filled out an online form, and made it through a written test in math and logic, interviews and a weekend workshop with simple coding drills, joining the 10-month program in 2016.

At Pursuit, Mr. Rosado, who has a two-year community college degree in liberal arts, got an intensive immersion in programming languages, concepts and projects. But the curriculum also covered so-called soft skills like making presentations, working in teams and writing résumés and thank-you notes.

Today, Mr. Rosado, 30, is an engineer at GrubHub, the meal delivery service, working on its smartphone software. In his previous jobs, in back office and sales associate roles in stores, he earned $15,000 to $20,000 a year. He makes nearly $100,000 now, he said.

Before Pursuit, Mr. Rosado, who is married with two young children, did not have enough to get by, living temporarily with relatives and sometimes in homeless shelters. Today, he and his family live in a two-bedroom apartment in the Bronx. Restaurant meals, movie outings with his children and a vacation to Florida last year are now within reach.

“Those are amenities that I never thought were possible before,” he said.

More than half of Pursuit fellows, as the venture calls its students, are on public assistance of some kind. Its classes are nearly half women, in contrast to many tech-training programs, which usually have far more men than women.