Chris Pratt Hopes Son Will 'Finally Think I'm Cool' After Seeing 'Guardians of the Galaxy Vol. 3' (Exclusive)

Chris Pratt is trying to reach superhero status in real life with his son.

The Marvel star, 43, attended the long-awaited world premiere of Guardians of the Galaxy Vol. 3 with Jack, 10, as "one of his dates" on Thursday.

Speaking exclusively to PEOPLE on the carpet, Pratt responded to whether or not he's achieved cool points as a dad for reprising his lead role as Star-Lord, saying, "No, not yet. Not yet. I'm hoping after tonight, he'll finally think I'm cool."

"Actually, he's here with me tonight. He's one of my dates tonight," added Pratt, who also brought his wife Katherine Schwarzenegger along for the high-profile event at TCL Chinese Theatre in Hollywood.

The dad of three, who shares Jack with ex-wife Anna Faris, then went on to talk about parenthood themes on-screen in the third installment, which writer/director James Gunn has said will be the last.

"The relationship between a parent and a child is definitely explored in this film, and there's no stronger bond than between a parent and a child," he shared. "And, yeah, certainly I can draw on my own experience as a parent when it comes to drawing and finding ways to be emotional and to push emotion."

As for his experience with his daughters, who she shares with Schwarzenegger, 33, Pratt describes what it's like at home being a girl dad to Eloise, 11 months, and Lyla, 2.

"Eloise is just starting to pull herself up. She's crawling around. She's saying, 'Dada.' She loves my guitar," said Pratt, who wore a lilac-and-gray-colored plaid suit to his premiere, with his wife in a metallic silver strapless gown with floral detail. Jack did not walk the carpet.

"Lyla's very, very sweet," he continued, of his oldest girl. Right now, what is she doing? She's a little sick at home, so I've been sleeping on her floor at night."

On April 5, Pratt shared more about being a girl dad during an appearance on Late Night with Seth Meyers. "I love it. It's fantastic," he told Meyers. "You know, you hear that maybe the experience is different and it really is, in my experience."

"My daughter Lyla is so girly. I picked her up yesterday and she said, 'Oh Daddy, that's a cute outfit. Look, you have little cute pockets,' ' he recalled, laughing, "That's not something Jack ever said to me."

While Pratt joked on Thursday about waiting for his son's approval of him as a cool dad, Pratt previously told PEOPLE that Jack "really freaked out" however when he saw his dad on the big screen as Mario in Super Mario Bros.

"He saw it already and he's thrilled. He loves it," Pratt told PEOPLE on April 1. "He took all his friends and he really freaked out."

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As for Guardians 3, in addition to Pratt, the film also features Zoe Saldaña as Gamora, Dave Bautista as Drax, Karen Gillan as Nebula, Pom Klementieff as Mantis, Vin Diesel as Groot, and Bradley Cooper as Rocket. Sean Gunn, Will Poulter, Chukwudi Iwuji and Maria Bakalova also appear.

Guardians of the Galaxy Vol. 3 is in theaters May 5.