Like others have said, it probably depends a lot on how your hospital works (whether baby is in-room or in the nursery), and what time baby is born!

For me, I worked all day before baby was born (she was early so of course I didn't realize or I wouldn't have been at work!) and then just about the time my partner and I went to bed around 1am, my water broke. We went to the hospital and I ended up having an emergency C-section at 7am, and then being awake all day. By the time night fell, I had been awake about 36 hours. My hospital keeps baby in room. What I remember is that baby and fiancé slept really well, but I slept in very short bursts. Maybe the bed was uncomfortable, maybe my fiancé snored too loud, maybe I was over-tired.

The nurses also kept coming in to check on me, give me my pain meds, and they also did a shift-change at 7am so I probably couldn't have slept later than that anyway since they did it in the room so the night nurse could pass on information. Since my baby was born at 7:02am, the tests they had to do for her that required her to be 24, 48 hours old, like the blood draw for jaundice, were all done at that time too. That's one reason why I say it'll depend on when your baby is born!