At 5-foot-10, Coco Gauff has the range, athleticism and touch to be a tennis champion.

But the 15-year-old star-in-the-making boasts another quality — one that she gleaned from her grandfather, a former minor league baseball player in the South during the 1960’s.

“He’s like the best possible grandfather I could have,’’ Gauff said after she debuted at the U.S. Open with a come-from-behind three-set victory Tuesday over Anastasia Potapova. “I’m just super grateful. He’s always calling me. My whole life he’s saying, ‘Never say die.’ Ever since I was younger I would hear that.”

Her U.S. Open debut was indeed tough as she committed three double faults in her first service game, fell behind 5-1, lost the first set and got broken to start the second set.

Gauff kept her poise and she now has a second-round meeting looming Thursday night at Louis Armstrong Stadium. She will face qualifier Timea Babos of Hungary, ranked 112th. If she gets through Babos, the Wimbledon sensation could face defending Open champion Naomi Osaka, the 21-year-old Japanese-American, in what would be a third-round spectacle.

Last month, Gauff advanced through qualifiers at Wimbledon and then reached the fourth round to move up to No. 141 in the rankings and receive a wild card to the Open’s main draw.

“I hit with Osaka at Miami Open three years ago,’’ Gauff said. “I remember I was complimenting her headphones because I saw she designed it. Like, these are pretty good. She’s doing amazing obviously. Hopefully I can get to her level.”

Like Osaka, Gauff has a solid support system and she speaks wiser than her years. Corey Gauff, her father, is her primary coach, though he played basketball at Georgia State and stopped playing competitive tennis early in high school. Gauff’s mother, Candi, is a former hurdler at Florida State.

But her grandfather has the most intriguing background — a minor-league baseball player in the Appalachian League with the Braves who once roomed with Dusty Baker.

According to USA Today, Eddie Odom played an integral role in desegregating Little League in Delray Beach, Fla., where the family resides.

Odom is also close to Coco’s younger brothers, budding baseball prospects.

“I can’t tell you how many times we’re eating dinner and he takes my brother out to go hit,’’ Coco said. “He even put a whole batting cage in his driveway just for my brothers.”

Ranked 875th when 2018 ended, Gauff’s newfound fame has been a lot to handle. She admitted to having nerves taking the Armstrong court Tuesday for her debut. Last September, Gauff was a favorite to win the Junior U.S. Open, but was upset in the semifinals.

“We had all that expectation last year in the juniors and now it’s back,’’ Corey Gauff told The Post with a touch of concern.

If you noticed cameras catching her father cheering wildly in the player’s box as the match wore on, it was at Coco’s urging. After she fell behind 3-0 in the first set, Gauff motioned to her family box. She thought her family was being too passive.

“I was telling them to get hyped up more,’’ Coco said. “I needed more positive energy. I was nervous. Just looking at them when they’re giving me a fist pump gives me a little reassurance. I think they were nervous. They wanted to stay more reserved too. I was like, ‘No, I need you guys to come on, stand up. I’m losing 3-love. I need something to help me.’ After a while they helped me.’’

Coco, who received a congratulatory tweet from Michelle Obama during Wimbledon, has impressed legend Rafael Nadal.

“I think she has great intensity playing,” Nadal said. “It’s tough to put a lot of pressure on her now. Even if she is doing amazing things, she is very young. She needs to internalize the things step-by-step. If not, it’s easy to lose the perspective. I really hope she has the right people around, and she will become a big star of this sport.’’

Her representative is Tony Godsick, Roger Federer’s agent, so it seems Gauff is indeed in good hands.