Sleeper at night?

P
My son is three weeks old and is on the bigger side.  He currently sleeps in his bassinet part of his pack and play but he's going to be too big for it shortly.  I'm trying to find a safe place for him to sleep for the next few weeks.  I'm scared to put him in the bottom part of the pack and play bc he can almost roll over on his side already.  I've tried his crib and he's just not ready to be alone and in that big of a space yet.  I've looked into a rock n play sleeper but I think he's just going to grow out of it too fast as well.