USA Boxing officials said team members would be selected after a series of tournaments next year.

Money, too, is a constant concern for amateur boxers, who must pay coaches and travel expenses. After the national tournament this week, USA Boxing will start paying the top two women in each of the three Olympic weight classes — $1,000 a month for the champion, and $500 a month for second place.

Without a sponsor or a stipend, Ms. Cruz has devised her own support system. She works part time as a secretary, which gives her time to train. Her father sometimes helps pay the rent on her sparse one-bedroom near Times Square.

Ms. Cruz spars at Gleason’s Gym, which is considered a hub of women’s boxing. Starting before 8 a.m. seven days a week, women wrap their hands, pull on gloves and start training.

Gleason’s opened its doors to women in the early 1980s, when Bruce Silverglade, the gym’s owner, persuaded his partner at the time to close the gym early three days a week to allow women to train. His partner was reluctant, but the gym needed the revenue.

“With women, they say, ‘Teach me the sport of boxing,’ and you can go from zero,” Mr. Silverglade said. “Every man is macho and thinks he knows how to box and how to be a fighter. We have to break down his bad habits. It’s much easier to teach the women, and they’re more hard-working.”

Women were not allowed to compete as amateurs on the national level until 1993, when Dallas Malloy, a 16-year-old from Washington State, sued USA Boxing for discrimination. The next year, six women registered to fight as amateurs in New York.

“It was a slugfest when I started,” said Cara Castronuova, 30, another boxer at Gleason’s with Olympic aspirations. “Nobody was interested in training women, so they didn’t get a chance to advance.”