When washing a newborns hair there's no need to really wash the hair of a newborn until they are around a few month of age.
Some babies are born with very little hair and it's not really that dirty but you can gently wash the newborns scalp and hair as soon as they are born and home when you give them a bath.
But they won't need a good hair scrubbing until around 6 months to a year of age.
Be sure to use some gentle baby shampoo when washing their hair and cover their eyes so they don't get any shampoo in their eyes.
I waited until my newborn was 4 months old before I even washed their hair because it really wasn't needed sooner than that.
It's usually not until around 12 months to 2 years of age until the baby has quite a bit of hair but some babies may be born with more hair than others.
Just gently wash the newborns hair or scalp if you want too but you only need to wash it every few weeks or so which is enough.