"Such precision Gus! Congrats you guys. Enjoy the most profound ride x," Carlton wrote.
"GUS!! We have a Gus in our family too! Congratulations!" Williams-Paisley said.
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Moore and Goldsmith married in November 2018 and announced in September that they were expecting a son.
"Baby Boy Goldsmith coming early 2021," Moore said on Instagram.
Moore said earlier this month that her birth plan had changed after her platelet count dropped dramatically.
Moore plays Rebecca Pearson on This is Us, which is in its fifth season on NBC. On Late Night with Seth Meyers in November, Moore discussed how the multiple timelines on This is Us made it impossible for her real-life pregnancy to match up with her character's.
"It's funny because the trajectory of our show is, we sort of jump around in time all the time," the actress said. "In fact, the very first episode I was in, we sort of took it back to going to the hospital to give birth to the triplets that day."
News broke Monday that Moore's This is Us co-star Justin Hartley finalized his divorce from his wife, Selling Sunset star Chrishell Stause, this month.
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