She’s a four-time Olympian. Her parents want her to get a real job.

Her parents are less enthused.

“We always try to convince her to stop playing," says her mother, Linda Liu. “We just want her to have a normal job."

It turns out even the most decorated American of all time in her sport can’t escape parental career pressure.

It’s an Olympic twist on the age-old conflict between children pursuing unconventional dream jobs versus parents pushing the 9-to-5. And besides enduring frequent and unsolicited professional advice from Mom and Dad, what’s most annoying to Zhang is that she concedes they have a point.

For every Simone Biles or Michael Phelps who turn Olympic success into a fortune, dozens more eke by in less glamorous sports. They fly alone, in coach, to far-flung matches on the international circuit, competing for meager prize money and sponsorships.

One losing streak or ruptured ligament could put an end to it all. “There’s so many things that can happen that can take away your stability in an instant," Zhang says.

The irony is that Linda Liu and Bob Zhang helped mold their daughter into a table-tennis star in the first place. Immigrants from China, they wanted to pass down their native country’s national sport to their offspring. So in a cramped Palo Alto apartment, the ping-pong table pulled double duty.

“It was also the dining table," Lily Zhang says. “We would just put a tablecloth over it and then eat."

A prodigy by age 10, she began spending summers in China, practicing with provincial teams that feed the national squad. To her, it was a chance to hone her skills and learn the secrets of why China has won 32 out of a possible 37 gold medals since table tennis became an Olympic sport in 1988: Chinese athletes train for up to nine hours a day, four times what Zhang does in the U.S.

But to her parents, table tennis was an opportunity to enhance her college applications. “If she played at a high level, it would help her get into a good school," says Liu, her mother.

At age 16, she competed at the 2012 London Games. Though she lost her first match, her parents declared it a resounding victory. “They’re like, OK, you got the Olympics, you got that on your college apps and now you can focus on studies,’ " Zhang says.

She mostly quit table tennis after that. Then, as a freshman at the University of California, Berkeley, she felt something was missing. She wanted to take a gap year and train for the next Summer Games.

Her mother disapproved.

“You already went to the London Olympics," Liu said at the time. “That is enough."

Liu says the conflict stems from both generational and cultural gaps. “We are traditional Chinese parents," she says. “We always want her to focus on school. I always wanted her to get a job and be a regular girl."

Team USA coach Jun Gao said this outlook has ended the athletic careers of other promising U.S. table-tennis Olympians, who have been mostly Asian-American. “A lot of Asian parents—that’s why you see so many talented players, no matter boys or girls, after they reach college, they say bye bye," said Gao, a silver medalist for China who started coaching U.S. national teams eight years ago.

Zhang understood why her parents, both Silicon Valley tech workers, wanted her to follow their lead. “They’ve had a hard life here," she says, “trying to make it here and make the American dream come true."

But she had her own dream of progressing with Team USA, even if it broke with conventions of many Chinese American families. “I play because it does make me happy, because it is one of the greatest passions in my life," she says. “I didn’t want to look back 30, 40 years from now and regret not taking that chance."

Mom and Dad eased off. “It is always her decision," Bob Zhang says. Then they helped her. They housed her for the gap year, paid for flights to competitions and cheered her on at the 2016 Rio Games, where she improved upon London by making it to the third round.

After graduating college with a psychology degree, she returned to the Olympics in 2021 and matched her finish in Rio. She then joined the pro circuit, flying without coaches or teammates to competitions with variable prize money.

This year, early exits in bigger tournaments in Jeddah, Saudi Arabia, and Chongqing, China, earned her $11,000 each time. But winning a competition in Manchester, England, netted only $650. She also gets income from her sponsor, table-tennis-equipment maker Joola.

The 19th seed and top U.S. table tennis player in Paris, Zhang has already gone viral. When hundreds of American athletes were on a boat during the Opening Ceremony, Stephen Curry brought Zhang and her teammates over to Anthony Edwards and told the brash young basketball superstar that these women would destroy him in ping pong, 21-0.

“I don’t believe it," Edwards said. “I’m scoring one point."

“No way," Curry said.

On Monday, she demonstrated why that idea is completely absurd. With Edwards in the stands, Zhang boomed two stunning forehands to upset Brazil’s Bruna Takahashi and advance to the round of 16 on Wednesday.

Zhang’s parents were also proudly looking on as she notched the biggest win of her Olympic career. But that doesn’t mean they have changed their view. “Being a ping-pong athlete is not stable," her mom says.

Nor have they stopped reminding their daughter about it. “They nudge me like, ‘Hey, what are you doing after Paris?" Zhang says. “What are your plans for jobs?’"

Write to Stu Woo at Stu.Woo@wsj.com