Keeping cat out of crib

My daughter is 5 months old. We’re in a very small living space so instead of a crib we had her sleeping in a travel bassinet on our bed with us, but she’s gotten too big for it so I’ve only just set up the pack and play next to our bed for her to sleep in until we move somewhere big enough for a crib.

The problem is, we have a cat (I already know some people are going to say we shouldn’t have the Cat anyway, but I disagree) and he keeps jumping inside of it. I haven’t put the baby in it yet, so I don’t know whether he’d try to get inside it with her. This cat is somewhat retarded and oblivious so I’m afraid he won’t have the common sense to not jump directly on the baby.

Is there anything I can do to try to keep him out of it while we’re sleeping?