I could see this as possible -- when puppies get tired, they just fall anywhere and no do more. A 4 month old baby can wiggle a bit, but I don't know (can't remember -- my son is 30 y/o) if a 4 m/o can shake off or somehow remove a puppy from his/her face or not.
All it would take is 2-3-4 minutes for that baby to be in big trouble. And no one would have heard anything if the pup was lying on the baby's face.
Tragic, no matter what the COD is. Four months old, oh my.
We have lost another precious one. SMH.