I think the rule of thumb is to wait until your baby can push a blanket away from their face or pull it away if it gets wrapped over their head. If they don't have the arm strength to roll over or push away from a smothering object like a blanket they can suffocate. That's why little babies are swaddled tight and not left with loose blankets just draped over them or put in sleepers that zip up and act as a blanket until they are strong enough to deal with a real blanket.
I played peekaboo with my daughter with a light blankly by putting it over her face and saying "where's the baby!" and she'd reach up and pull it down and giggle like crazy. It taught her how to pull the object off her face if it was there.
Before babies can just barely roll over on their own don't have the arm strength to get out of a blanket tangle if they manage to get into one.
Same thing with stuffed animals. If they roll over and their face gets smooched into the fluffy plush of the stuffed animal and they can't push away from it, they'll smother.
There’s no right age to say because it all depends on the physical development of your own child. You have to make the call based off what you feel comfortable with.