Can your baby self soothe to sleep?

My wee boy cant initially fall asleep himself, he needs rocked and shooshed but once he is asleep he can self soothe through the night if he is in a semi awake state by sucking on his fingers. We stopped giving him a dummy in the night when it fell out and he gravitated to self soothing this way.

Yeah ive noticed my little girl can self soothe through the night occasionally...other times needs the boob but getting to sleep initially is virtually impossible. Ive tried to avoid feeding her to sleep, putting her in the next to me drowsy but awake, settling her in the next to me but none of it works...She'll only fall asleep in my arms, in a sling, in a pram or in a car. We still have a lot of night time wake ups so I know its key to reducing these but can't seem to get something that works for her