The former 30 Rock star and the yoga instructor announced their son's arrival via their social media accounts on Wednesday (17Jun15) by sharing a picture of a baby's hand clutching a finger, and hours later the proud dad attended the 2015 Fragrance Foundation Awards in New York City and gave his first post-birth interview to TV news show Extra, which often features his wife as a correspondent.

Baldwin said, "It was amazing. We came into town for Hilaria to go to the doctor on Monday. I'm doing this play on Long Island (and) I'm off on Monday, so we come in for her to go to the doctor.

"We go to the doctor, every thing's fine, she goes to dinner with her friends, every thing's fine, wakes up Tuesday morning (at) 1.30 in the morning, not feeling good, then 2.30 in the morning feeling really lousy... We go to the doctor at 9.30 in the morning, he says come back at two and I'll tell you if it's real, and she's like I'm gonna punch this guy; if this isn't for real I don't know what it is for real.

"We go back at two and they admitted her and she had the baby at 1.30 this morning... I'm not gonna get into too graphic of detail, but I was on the team... Someone else is doing all the hard work and you're there for them... You sit there and go, 'I would do anything to make this easier for you'. My wife is really... she's my hero; she's tough."

Baldwin will be back onstage for a production of Arthur Miller's play All My Sons in East Hampton, New York on Thursday (18Jun15).

Rafael is the actor's third child - his daughter Carmen was born in 2013 and he has a 19-year-old daughter, called Ireland, from his marriage to actress Kim Basinger.