Scarlett Johansson had a little help bonding with her Asteroid City co-stars, thanks to her son Cosmo.

When Johansson, 38, was working on the Wes Anderson film, Cosmo — who will turn 2 years old in August — was just a little baby, and everyone loved spending time with him. According to Johansson, he was quite the popular little guy on set.

“I actually wasn’t popular, it was just the baby,” Johansson tells PEOPLE exclusively of her son with husband Colin Jost. “People were excited to see the baby, not me. They’re like, ‘Oh, it’s you. Where’s baby?’ ”

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Cosmo and Jost both spent time with Johansson in between takes. “My family came [with me to set],” she recalled to PEOPLE, adding, “My husband and baby did because we had just had a little baby.”

“Some people had partners that came up,” Johansson continued. “Most people were alone, I think. A lot of people had children too, but maybe a little bit older.”

“I just had a tiny, tiny baby,” she said, adding that Cosmo was like the “set baby.”

Jason Schwartzman had a theory of why. “I think people are excited to see the joy,” he told PEOPLE.

Scarlett Johansson Reveals Special Connection Between Son Cosmo and Daughter Rose’s Names

In September, Johansson shared the meaning of Cosmo’s name and the special connection between the moniker and her 8-year-old daughter’s name, Rose Dorothy. “They are both flowers,” Johansson told Kelly Clarkson. “Not a lot of people make that connection. Cosmo is a really sweet little flower that comes in different shades of orange and yellow.”

“That’s why my daughter liked it too,” she added.

Johansson connected with the name Cosmo because she said it seemed “refreshing.”

“It’s so charming,” she explained. “Our friends all liked it.”

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Though, it did take a while for Jost’s mom to come around to it. “She kept suggesting other versions of it and I’m like, ‘No, he’s already here, he’s out.’ ”

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Johansson and Jost married in an intimate ceremony in October 2020. The pair got engaged in May 2019 after two years of dating.