PHOENIX — Deandre Ayton was a 6-foot-5 12-year-old at the 2011 Jeff Rodgers’ Basketball Camp in Nassau, Bahamas, when he watched in awe as one of his counselors drilled three-pointer after three-pointer from the top of the arc.

Still somewhat naive about the NBA, Ayton didn’t know that it was Warriors rookie guard Klay Thompson putting on the shooting clinic. All Ayton knew was that he wanted to be like him.

“I was just so shocked and blown away,” Ayton said. “Just seeing him shoot and just being around him, it was a great feeling.”

Now the Phoenix Suns’ starting center as a rookie, Ayton, 20, credits Thompson for helping pave his path to the NBA. Never mind that Thompson wasn’t born or raised in the Bahamas. The son of Bahamian basketball legend Mychal Thompson, Klay has long taken pride in his island heritage and is considered a de facto member of the country’s NBA fraternity.

Thompson returns to Nassau, the capital city of 266,100, for a week each July to visit his father’s side of the family and help out at the basketball camp. His family’s foundation plans to start a youth camp there next summer. Mychal has talked to the Bahamian government about trying to help fund an 8,000-seat arena in Nassau, which could host NBA preseason games, premier AAU showcases and college tournaments.

The Bahamas’ top gym, the Kendal G.L. Isaacs National Gymnasium in Nassau, is out of date with a seating capacity of 2,500. Battle 4 Atlantis — a preseason college basketball tournament held each November on Paradise Island — plays its games in the converted grand ballroom of an ocean-themed resort.

The country’s interest in the NBA far exceeds its resources for grooming NBA prospects. Thanks to minimal basketball infrastructure in the Bahamas, promising local players like Ayton and Sacramento Kings guard Buddy Hield attended high school stateside to attract college recruiters’ attention.

“They just need more organizations as far as grassroots basketball,” said Klay Thompson, who estimated he has 40 relatives spread between Nassau and Hield’s hometown of Freeport. “But, trust me, there will be more Deandre Aytons and Buddy Hields to come. There’s just too much talent down there.”

When Mychal Thompson was growing up in Nassau in the 1960s, baseball — not basketball — was the country’s sport of choice. It wasn’t until he stood 6-foot-5 at age 15 that he relented to his older brother Colin’s urgings and joined their church team. Seven years later, after a standout career at the University of Minnesota, Mychal became the first non-American to go No. 1 overall in the NBA draft.

Mychal, who won two championships with the “Showtime” Lakers of the 1980s, made sure his three sons — Mychel, Klay and Trayce — felt connected to their Bahamian roots. Summer vacations were spent challenging the locals to pickup games at the national gymnasium, fishing off the coast of New Providence Island and dancing at family parties in Nassau.

Klay attributes his laid-back personality to his Bahamian heritage. Like many of his Caribbean relatives, he practices a simple lifestyle aimed at minimizing stress and maximizing fun.

“We try not to sweat the small stuff,” said Mychal, who has a street named after him in Nassau. “We try to relax, have a good time and look at the positive side of life. Klay always looks at the positive side of life.”

Of the five Bahamian-born players who have suited up for an NBA game, none have made an All-Star team. That could soon change. While Hield leads the upstart Kings with 19.9 points per game, Ayton — the No. 1 pick in June’s draft — has a chance to become a transcendent big man. At 7-foot-1, 250 pounds, he moves like someone much smaller, gliding into the key for put-back dunks, alley-oops and blocks.

Klay Thompson knew Ayton was destined for greatness when he saw the gangly preteen dominate his peers at that 2011 camp, but even he didn’t foresee this. In 38 NBA games, Ayton is averaging 17 points (on 60.5 percent shooting) and 10.9 rebounds.

Late Monday night, after watching Ayton go for 25 points and 10 rebounds in a loss to his Warriors, Thompson posted a picture to Instagram of the two embracing at midcourt. Above them, in white letters honoring Bahamas’ area code, was written: “#242 to the world.”

“Obviously, we have the utmost respect for each other,” Ayton said. “We both know where we came from.”

Connor Letourneau is a San Francisco Chronicle staff writer. Email: cletourneau@sfchronicle.com Twitter: @Con_Chron