Same problem: the child account only has an EA ID with a password, it cannot have an email or phone number which are the only identifiers the login page accepts (there is no "login with EA ID" option at "signin.ea.com"). So even though I am the one who sets up the child account and I know the password, I have yet to find a way to do anything with the account because there is no way to login.
Upgrading to a "teen" account (age 13 here in the US) sounds like it will allow you to add an email address which would let you invite the account into the "family management" section (I cannot for the life of me understand why child accounts aren't automatically part of "family management" like every other platform). No idea if that is feasible because I basically lost the EA ID my son wanted to the child account and gave up.
