Ice Cube did not get this far by thinking small. Witness his latest project — a 3-on-3 basketball league set to barnstorm across America starting Sunday at Barclays Center.

So ask him about his future player wish list for “BIG3” and he responds as many Angelenos would: “He used to wear No. 8 and used to wear No. 24,” the pioneering rapper and actor said. “That would be a dream.”

That would be Kobe Bryant. But Ice Cube accepts that to get from here to there, the league must establish itself as something more than the passing whim of a celebrity sports fan, and thus he is taking a long view.

“This isn’t a rapper deciding to do a basketball thing because it seems like a good way to make money,” co-founder Jeff Kwatinetz said. “This is someone who thought this out.”

Kwatinetz said if he wakes up at 6, he already is late for work, because Ice Cube has been emailing him since 5:30.

“I’m not kidding,” he said. “If that was a one-day occurrence, I wouldn’t bring it up. It’s common. One day this week, I slept until 7:30 a.m., God forbid. I was 250 emails behind.”

advertisement | advertise on newsday

Ice Cube said he never has worked harder at anything in his career.

“Just because we have to do everything so fast,” he said. “We had six months to build a league, promote a league and market a league with just a pool of great people, dedicated to seeing this work.”

So what exactly is BIG3? It is 3-on-3 halfcourt basketball, a version of the sport played more commonly than the 5-on-5 fullcourt game customarily seen on television.

To make that marketable, BIG3 signed the likes of Julius Erving, Charles Oakley, Rick Barry, George Gervin and Clyde Drexler as coaches and Kenyon Martin, Rashard Lewis and other familiar names to play.

Oakley, 53, also is slated to play, although he was cagey when asked about that on Friday.

NBA videos

“I might play and sometimes I probably won’t,” he said. Told he looks to be in shape, he said, “You can have a paint job, but the body needs work.”

Perhaps most intriguing: Allen Iverson, 42, will coach and play for a team called “3’s Company.”

There will be quadrupleheaders each Sunday that showcase the eight teams in four games, with the championship set for Las Vegas on Aug. 26.

There are two-, three- and four-point shots. First to reach 60 points wins, but you must win by two.

Lewis, captain of “3 Headed Monsters,” said that when commissioner Roger Mason Jr. explained it all to him, he considered it a “no-brainer.”

advertisement | advertise on newsday

“As a kid growing up, when you play basketball with your friends in the backyard or on the driveway, it’s 2-on-2, 3-on-3,” he said. “You’re hardly ever playing 5-on-5 unless you’re in an organized game.”

Lewis is the kind of player Ice Cube had in mind for this — a two-time NBA All-Star who is only 37 but whose career ended in 2014 because of a bum knee that is fine for halfcourt but not for 5-on-5.

“As a pro player, your game never really leaves, but your body tells you otherwise,” Lewis said.

The atmosphere at the league’s first media day Friday at Chelsea Piers in Manhattan illustrated its vibe, as former pros greeted each other warmly, recalling long-ago games with and against each other.

Ice Cube seemed to revel in it, anticipating a league that will be fun for participants and fans during the summer sports doldrums.

advertisement | advertise on newsday

“Man, I feel like Walt Disney sometimes, because I feel like I’m doing something that’s going to make a lot of people happy,” he said. “I feel like when they see this on Sunday, they’re going to wonder, how did we live without it, because it’s so cool, so good.”

Barry, coach of the Ball Hogs, said, “The adrenaline gets going, the competitiveness comes out, and I think people are going to be very pleasantly surprised because it’s going to be very fast-paced, fast-action stuff.”

Fellow former Net Erving, coach of Tri-State, said he has been asked by fans and journalists if he would like to play and whether he still can dunk at age 67, all of which he called “not an adult conversation.”

The league has more going for it than most sports startups. That includes a TV deal in which Gus Johnson will call the games on FS1, which will show them on delay Monday nights. The championship will air live on Fox.

Comedian/actor Michael Rapaport will be the sideline reporter. “I talk a lot of trash,” he said. “They’re already calling me the Howard Cosell of the BIG3, but I’m humble.”

An unexpected boost occurred earlier this month when the IOC added 3-on-3 hoops to the Olympics for 2020.

“The fact that it’s in the Olympics now, this makes the world pay attention,” Ice Cube said.

Above all else, BIG3 has a drawing card in Ice Cube himself. At 48, he has cross-generational appeal and ongoing cultural cachet.

“When Roger told me Ice Cube was behind it, everything he pretty much touches turns into gold,” Lewis said.

Ice Cube said competitive credibility is essential for acceptance. He expects “hard-nosed basketball” from prideful old pros. “They don’t want to get out there and embarrass themselves,” he said.