Not too long after James Gunn and Peter Safran stepped up to lead DC Studios into the future, they were riffing about Supergirl. The Tom King comic series, “Supergirl: World of Tomorrow” was one of the ideas they were especially excited about, and Gunn had a very specific image in his head.

He just didn’t yet know her name.

“He goes, ‘you know the young girl from ‘House of the Dragon’? The young queen or princess? That’s how I picture it, like a young punk rock girl who is just totally badass and tough,’” Safran told The Associated Press. “I was like, yeah, that sounds fantastic, and we haven’t seen that before.”

Milly Alcock, now 26, had just started to break out playing Princess Rhaenyra Targaryen (later portrayed by Emma D’Arcy) in the “Game of Thrones” prequel, when she got a request for a self-tape for the secretive Supergirl project. Alcock had been working in her native Australia since she was a teenager, but her world was suddenly getting bigger very quickly.

A few weeks later, she was summoned for a screen test (her first ever). She boarded a 24-hour flight from Sydney to Atlanta and gave it her best shot.

“I kind of had a feeling, I remember I like got back to my hotel room and I like sat down and I was like, ‘Oh, this is gonna, something’s gonna happen,’” Alcock said. “I just had like an intuition that like, this is going to be a very exciting challenge if it goes in my favor.”

‘This is crazy, what have I done?’

Ten days later, Gunn texted her an article in the trade publication Deadline: “‘Supergirl’: New Woman Of Steel Is ‘House Of The Dragon’s’ Milly Alcock.” No phone call. No context. And all she could think was, “This is crazy, what have I done?” A few days later, she was back on that 24-hour flight to film her cameo in “Superman.”

And things have not slowed down. If shooting the film was a marathon of stunts and action and emotion, the promotion of new DC’s second major film is going to be its own non-stop ride.

When Alcock spoke to the AP earlier this month, she had just arrived in Las Vegas from Kyoto, where she was filming another movie, and on just two hours of sleep had to muster the energy to get up on stage in front of thousands of movie theater owners to hype “Supergirl,” which is out June 26.

“It’s a really original and unique take on a superhero movie,” Safran said. “I think it’s just a great movie for audiences. It’s not just for superhero fans.”

‘She’s just that girl’

The character might be less widely known than her famous cousin, but the response to her appearance in “Superman” was encouraging.

“She’s in the ‘Superman’ movie for, you know, 12 seconds, yet one of the things audiences wanted to see ... more of was her,” Safran said. “And Milly in real life, she’s just that girl … she is authentically a badass.”

Perhaps part of the intrigue is that she’s not straightlaced Superman, who got to be raised by loving and gentle parents on Earth. Supergirl saw her planet destroyed and everyone she knew killed and had to fend for herself.

Directed by Craig Gillespie, best known for two other films about complicated young women, “I, Tonya” and “Cruella,” this film finds the jaded Kara on an intergalactic odyssey with Krypto the Superdog and a young woman seeking revenge against the murderous Krem of the Yellow Hills.

“Kara surprisingly reminded me a lot of myself, which I never thought I would get from playing like a superhero, from playing someone who isn’t human. There’s a lot of humility in her and that kind of made me fall in love with her immediately,” Alcock said. “Sometimes you can get swept up in what other people expect, and then you kind of lose your intrinsic you-ness. And that’s why people hire you in the first place, because of what you bring to something just innately being who you are.”

‘Why would someone have a toy of my face?’

Alcock didn’t grow up a big film fan, but in acting found a lifeline and an outlet to communicate feelings that she struggled to in real life. It helps her exist as a person, she said.

Recently, Alcock has been living in London, where she said she has a great group of friends, none of whom are actors. And she’s adjusting to the reality that her face is going to be everywhere for a bit.

“It’s been kind of disorientating,” she said. “I do this job because it gives me the ability to disappear. So then to like suddenly be so visible and so exposed is a very vulnerable experience. I’m just trying to learn how to deal with that relationship. But I mean, it’s exciting. Of course it’s exciting. But like anything exciting, it’s also terrifying.”

When she was on the “Superman” set, she remembered talking to David Corenswet briefly and realizing that they had very different perspectives about the experience.

“I remember him being like, ‘We’re gonna have action figures, isn’t that cool?’” she said. “And I was like, ‘That’s so weird. Why would someone have a toy of my face?’”