I slept on my tummy the night I had my son in the hospital! (: as long as there's no concerns and you didn have a c-section you're probably fine!
Your breasts might be a little sore but other than that, go for it! I can't wait to stretch out and lay on my belly after this bowling ball is born!! Ugh...so jealous!
My second night in the hospital I looked at my husband and went "OMG I CAN SLEEP ON MY STOMACH AGAIN!!!!" So I did lol. As long as you're comfortable and no issues go for it momma!
I slept on my stomach 3 days after my son was born, aside from the swollen Boobs it felt like heaven lol....