Can your baby sleep on their own?

At what age ur baby sleep on their own and what’s the cue? My baby is 2 months old and she somewhat can sleep on her own, but hor she will move non stop, keep touching her face (sometimes have scratch). I dont need to put her drowsy but awake, jus put her on bed and off light then she will do those actions. So wanna know anyone else LO have different cue?