S.H.
Both my kids, liked the Fisher Price "Ocean Wonders" crib toy/musical toy.
And they'd turn it on themselves or turn it off when they were done, if they didn't fall asleep by then.
Or, instead of something entertaining them, we'd have baby safe stuffed toys in the crib with our kids. They loved that. They'd entertain themselves, and found it cozy and comfy to have "friends" in the crib with them... and for my son, one of the stuffed toys became his "lovey" that he'd hug and sleep with.
But, it was from about 6 months old, that we'd have those stuffed toys in the crib with them.
Or, put on white noise.
Keep everything dark, when the baby naps or sleeps.
Also, some babies will just fall asleep on their own, playing with their fingers or babbling to themselves first, and whatnot. Its a way that a baby winds-down and falls asleep. Both my kids did that too.
But many times, a baby won't fall asleep right away the second their head hits the pillow... it can take time. BUT, if the baby is doing fine sort of self-soothing/babbling to themselves to drift off to sleep, that is fine too. Let them. Falling asleep, is not always a "quiet" still as a statue sort of thing, with a baby.
But, with both my kids, the Ocean Wonders toy was something they really liked and it lasted a LONG time and grew with them.
Good luck,
Susan