Cats around baby 🐈

Lo
We have two rambunctious cats that also love to cuddle. I am paranoid about them laying on our baby's face or something! My co-worker said her cat never went near her infant daughter and I felt better. I will train them to stay out of crib as soon as I get it, and I plan on locking them out of our room/nursery when baby is sleeping. Can anyone add any comments about this?