Looking barely older than the players who attended his introductory news conference at Memorial Gym on Monday, USF head basketball coach Todd Golden discussed the goal of returning the Dons to the prominence they enjoyed from the 1950s through ’70s.

“The most important (things) are the vision and the belief,” Golden said in an interview following the news conference. “You can’t get there unless you really believe you can do it. … We’re just not going to rest until it gets done.”

Golden, 33, got his first head-coaching job Wednesday when USF named him to replace Kyle Smith, who left the Hilltop after three seasons to become the head coach at Washington State. Golden had been on Smith’s staff for those three seasons.

“It is important to make the right hire, not the safe hire,” USF athletic director Joan McDermott said. “We could have done a national search, but we would have come back to Todd Golden.”

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The main news Monday was Golden’s announcement that Bill Cartwright has agreed to become a special assistant to the program. Cartwright was a center who helped the Dons to those lofty heights in the ’70s before winning three NBA titles as a player with the Chicago Bulls in the 1990s.

“I want him to be as involved in the program as he can be,” Golden said. “I want him to mentor myself and our staff.” Cartwright, who returned to his alma mater three years ago as the director of university initiatives, won’t be an on-the-court coach or an on-the-road recruiter.

Golden, a guard for head coach Randy Bennett at St. Mary’s for four seasons (2004-08), recruited several of the 10 scholarship players who will return to the Dons next season.

“He cares a lot for the guys. He cares a lot for the community,” said center Jimbo Lull, who will be a senior next season. “I know a lot of these guys here respect him, and I think he’s definitely earned a lot of our respect. He’s just a really good dude.”

Golden said he will continue to stress the goals set by Smith, whose teams won at least 20 games in each of his three seasons and also did well in the classroom.

“During this transition, I’ve made it as clear as possible to (the players) that these high standards and demands that we hold them to will not change,” Golden said. “They understand that it’s a privilege — and not a right — to wear the USF name across their chest.”

Swingman Jordan Ratinho, who also will be a senior next season, believes the fact that the Dons have so many returnees will make it smoother for Golden as a first-time head coach.

“It’s not like he’s going into a new program and trying to lift everything up from the ground up,” Ratinho said. “Here, he’s got his team. Everyone — 10 guys coming back — respects him and wants to play for him.”

Golden also will keep a good portion of Smith’s staff. Golden elevated Kevin Hovde to associate head coach. Jonathan Safir will stay in his role as the director of basketball operations.

And, Ralph Ferrari, the brother of departing point guard Frankie Ferrari, will remain with the program in a yet-to-be-determined role. Ralph Ferrari was a student manager in the 2017-18 season and was the video coordinator this past season.

Steve Kroner is a San Francisco Chronicle staff writer. Email: skroner@sfchronicle.com Twitter: @SteveKronerSF