Jay-Z Out and About for First Time Since Birth, Good Sign for Twins' Recovery?

Jay-Z is out and about in L.A. and smiling like the proud new dad he is ... which could mean there's good news where Beyonce and the twins are concerned.

Jay was in West Hollywood Monday morning -- the first time he's been spotted away from the hospital since Bey gave birth almost a week ago. TMZ broke the story ... the newborn boy and girl have remained in the hospital due to a "minor issue."

Unclear what Jay-Z was doing, but he was leaving a complex that has a SoulCycle ... and we know he's been known to get his SC on from time to time.

We're told he's been at the hospital with Bey and the twins nearly round the clock, and was seen arriving there early Monday morning.

He didn't have much to say to photogs outside SoulCycle, but we're hoping the smile said it all.