could try Spotify baby white noise to help your baby to sleep. currently, I using this (https://open.spotify.com/track/10CRc1rvEXATSXu6iwZ7AJ?si=QAePihDnSdey_rV-h_Dukg) for our kid, we usually leave the kid alone in his cot after we swaddled and fed him. coupled with the white noise, he would fall asleep quite fast. our kid is only awake when he is hungry and that's when we changed his diaper as well
Going through this too now. 1am-3am didnt sleep. Slept and woke up every now and then 😭