Michael Che Shares Why He Isn't Interested in Babysitting Colin Jost and Scarlett Johansson's Son

Colin Jost and Scarlett Johansson welcomed their first baby together, son Cosmo, they announced in September

Michael Che isn't rushing to babysit Colin Jost and Scarlett Johansson's son anytime soon.

The Saturday Night Live star, 38, appeared on Monday's episode of The Tonight Show Starring Jimmy Fallon where he explained why he'll be keeping his babysitting duties to a minimum despite Jost and Johansson's son Cosmo being a "cute kid."

"It's an adorable baby," Che says of the couple's son, whose birth Jost announced in September.

Still, Che says he doesn't have much of an interest in babysitting as "babies are fun for like a second."

"You know, they don't do much after you've looked at them and they're just staring at you trying to keep their head on straight," he says. "It's like, 'Get this wiggly thing away from me.' "

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"I don't like babysitting," he adds, though he notes that he's "actually a great babysitter."

"I've been babysitting my whole life. I have nieces and nephews that are like three years younger than me. I've been babysitting them since they were babies. Since I was a baby, actually," he teases.

As for his babysitting technique, Che shares, "I just let you cry until you're sleepy."

After PEOPLE confirmed that Jost and Johannson welcomed their first baby together in September, Jost then gave more insight about their new family of four.

"Ok ok we had a baby. His name is Cosmo. We love him very much. Privacy would be greatly appreciated," he wrote on Instagram, then joking with his SNL costar Che, "For all inquiries please contact our publicist @chethinks." He also added the hashtags: "#wegotawaywithitforalongtime" "#nokidspolicy" and "#weregoingtodisneyworld."

A source told PEOPLE at the time that Jost and Johansson — who is also mom to 7-year-old daughter Rose Dorothy — are "both so happy and madly in love with the baby."

"They wanted this child who will fit right into their lives since they already have her daughter," the source said. "They are an awesome couple, both talented, smart and clever. They will be the best parents. Colin is considerate and helpful in everyday life so adding one more to the mix should be fine. The baby is the best thing ever for both of them."