“I don’t see any fundamental weaknesses, but I’m sure her dad and her team have a lot of areas that they’re going to try to strengthen over time,” said Martin Blackman, the general manager of player development for the United States Tennis Association.

“The most promising component of where she’s at right now is the fact that her parents and her team have a long-term perspective, and that means she’s going to make good decisions on taking care of her body and not overtraining,” Blackman said.

Gauff’s skills, especially her intensity and focus, first surfaced so conspicuously and consistently in Atlanta. There, the 7-year-old girl who would fall asleep during drives to a tennis center south of downtown would begin a dynamic warm-up without coaxing. She talked about winning Grand Slam tournaments, scrutinized the Williams sisters, showed herself to be a quick study and would do handstands and cartwheels during breaks in practice.

“She was a natural competitor in that she just wanted to win and never ever, ever, ever quit,” said Jewel Peterson, who coached Gauff in Georgia. “One of the things that you’ll see with younger players is that if it’s not going the way they want it to go, they’ll quit fighting. That was never her.”

Most young players, Peterson said, took group lessons while music from animated movies played in the background. But Gauff could handle more sophisticated training, like refining the grip for her serve.

The Gauffs saw Florida, long an outpost for elite tennis, as the place where Coco’s early potential could best be cultivated. Beyond tennis, it offered family ties . Gauff’s maternal grandmother, Yvonne Odom, integrated a local high school in 1961, and a decade later, Gauff’s grandfather, Eddie Odom, founded a Little League that was open to black children (a baseball field in Pompey Park is named for him).