Kanye West All Smiles After Birth of Baby Girl

1/16/2018 12:57 PM PST

Kanye West Seen For First Time Since Birth of Daughter

Kanye West isn't wasting any time getting back to work ... heading into the office just a day after welcoming his new baby girl.

West was spotted outside his Calabasas studio Tuesday -- and while he stayed quiet -- he still cracked a big smile when photogs congratulated him on the birth.

TMZ broke the story ... Kim and Kanye were in the hospital room when their surrogate gave birth to a 7 lbs 6 oz girl at Cedars-Sinai early Monday morning. Kim was the first to have skin-to-skin contact with the baby, and Kanye held her shortly after.

Still no word on a name.