“Today I have my wits about me,” James Gunn said. “I was going to die yesterday, I was so tired.”

It was two weeks before the release of “Superman,” and I had met Gunn at the film’s Los Angeles press junket, just one stop on the director’s whirlwind, worldwide media tour. At the time, he was hopeful that the movie would connect with audiences, and it certainly has: “Superman” opened last weekend with $125 million at the domestic box office and earned an A- CinemaScore from audiences.

Still, that success barely affords Gunn the opportunity to sleep any easier. “Because this is our first DC movie and I’m also the head of the studio,” he said, “I haven’t had a day off work for months.”

Best known for directing Marvel’s “Guardians of the Galaxy” movies, Gunn was initially lured to DC Studios in 2018, when Marvel fired the filmmaker over resurfaced tweets. Though he was eventually rehired to finish the “Guardians” trilogy, his work on DC projects like “The Suicide Squad” and “Peacemaker” impressed the Warner Bros. Discovery chief executive David Zaslav, who tapped Gunn to run DC Studios alongside the producer Peter Safran.

“I’ve always had this desire to create a fictional universe,” said Gunn, 58. “I got hints of that with ‘Guardians’ and the cosmic universe of Marvel, but since I took on DC I knew that I was just going to have to go crazy for the first few years.” That commitment meant juggling many major projects simultaneously: At one point, Gunn was filming both “Superman” (with David Corenswet in the title role) and the second season of “Peacemaker” (starring John Cena and Gunn’s wife, Jennifer Holland) while also overseeing forthcoming DC projects like the film “Supergirl: Woman of Tomorrow,” out next year from the director Craig Gillespie.

“I also had to resign myself to the fact that I can’t do everything,” he said. “I give notes on all these other projects, but I can’t micromanage” them all, even though, he added, “I always want to do more. That’s been difficult, finding at least some boundaries.”