My midwife told me I had to wait till it had completely dried out before I bathed my son to reduce the risk of infection and prolonged healing times so for the first week after the cord fell off we just gave him bed baths x
@Zariah in the UK we’re told not to wet it or clean it, and we’re told to either avoid baths (and just wipe baby down) or bathe baby but avoid the cord: https://www.nhs.uk/conditions/baby/caring-for-a-newborn/washing-and-bathing-your-baby/#:~:text=You%20only%20need%20to%20wash,talking%20while%20you%20wash%20them. x
I still waited about a week after it fell off to allow the skin to heal!
Sponge baths only while not getting the belly button wet
You could have bathe baby while the cord was on just made sure that you dried it and cleaned it with alcohol so it can heal properly