NEW YORK >> For every Naomi Osaka and Coco Gauff who achieve early success, there are dozens of players who struggle through low-level tournaments to earn berths at big events and career-sustaining paychecks.

New York native Kristie Ahn, a wild-card entrant at the U.S. Open, made her Grand Slam debut here in 2008 but didn’t win a major match until this week. Today, the 27-year-old Stanford graduate reached the fourth round with a 6-3, 7-5 victory over Jelena Ostapenko and sobbed in joy on the Grandstand court.

“I’d be lying if I said, like, ‘Oh, yeah, I’m so happy I didn’t find success right away,’” she said. “But to be transparent with myself, as well, I don’t know if I ever would have gotten this far if this had happened at a different time in my life. I feel like I’ve had a lot of closure with myself in different scenarios.”

Taylor Townsend, 23, was the top junior player in the world when U.S. Tennis Association executives refused to pay for her trip here in 2012 for “health reasons.” Translation: They thought she was overweight. She got into the Open this year as a qualifier and today, two days after she upset Wimbledon champion Simona Halep, Townsend advanced to the fourth round with a 7-5, 6-2 victory over Sorana Cirstea at Louis Armstrong Stadium. She came to the net 106 times against Halep and 75 against Cirstea, confident in her serve-and-volley game. She’s confident in herself, too.

“I wouldn’t change anything because I appreciate so much where I am, because I know where I came from. And I think it’s easy for people to forget where they came from,” she said. “I went one year and I won four matches in a calendar year. So I understand and I’m appreciative where I am and the growth I’ve made, because you’re able to kind of say this is where I came from and be able to not go through those same things again and you can kind of learn from your mistakes and move on.”

Croatia-born Donna Vekic knows the pitfalls of being a phenom. She cracked the top 100 when she was 16 but slipped and is still regaining her footing at age 23.

“I was putting so much pressure on myself. I thought I’d be making finals every week. That was not the case,” said Vekic, who reached the fourth round with a 6-4, 6-1 victory over Yulia Putintseva of Kazakhstan. “There were so many improvements to make and I definitely wasn’t aware of that when I was 16. There are a lot of amazing young girls coming up. I hope they have a good team around them that knows how to guide them in the tough times.”

Bianca Andreescu of Canada, 19, continued her rise with a 6-4, 6-4 upset of Caroline Wozniacki. Andreescu, the highest-ranked teenager on the tour at No. 15, will face Townsend next.

“You see a lot of young players doing really well right now, and I think it’s really good for the game,” said Andreescu, who had shoulder problems after she won the Indian Wells title in March. “You see many fresh faces, and I think we’re only going to get better from here.”

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Nadal cruises

No. 2 men’s seed Rafael Nadal hasn’t spent much time on the court here. He won his first-round match in straight sets and his second-round match by walkover before he beat Hyeon Chung of South Korea 6-3, 6-4, 6-2 today. Nadal didn’t face a break point in reaching the fourth round here for the 11th time.

Whether it’s better to be rested or to play a lot and become match-tough is a toss-up. “You never know what’s better or worse, no? I am happy to be where I am. I’m in the fourth round, and that’s the main thing,” said Nadal, a three-time U.S. Open champion.

His next opponent will be Marin Cilic of Croatia, who ousted No. 14 John Isner of the U.S. 7-5, 3-6, 7-6 (6), 6-4.

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Etc.

No. 26 Julia Goerges upset No. 7 Kiki Bertens 6-2, 6-3 to earn a fourth-round slot against Vekic. … No. 13 Belinda Bencic advanced when No. 21 Anett Kontaveit withdrew because of an acute viral illness. … Men’s No. 6 Alexander Zverev reached the fourth round by defeating Aljaz Bedene 6-7 (4), 7-6 (4), 6-3, 7-6 (3).