My first baby lost a ton of hair a few weeks after she was born it just thinned out a ton. I don't think there is anything you can do about it. But she's 3 now and her hair is nice and beautiful it goes all the way down to her tush. If she does get cradle cap the only think that worked for my girls were using head & shoulders And then I would put coconut oil or baby oil on after and comb Out the flakes.
You don't need to put anything in her hair. It'll grow out out by itself.
Some babies hair just thins or falls out. It'll grow back. Theres really not a whole lot any person of any age can do to make hair grow except take biotin and its really not all that good for you.