No, you shouldn’t put anything in his cot . Although baby can’t hold his head, and can’t flip back, they can sleep on stomach , lying on the side of the face (that won’t suffocate).
What I did last time is I will wake up periodically to check on baby, and if baby wake up for night feed, i will wait for baby to slp before I go back to slp (in case they flip and can’t flip back).
Raven Tan