Unable to convert an Apple ID to use it with child account

Contact Apple ID Support for assistance.  See the Apple Support articles below for contact information.  

Apple ID - Official Apple Support.   -

Contact Apple for help with Apple ID account security - Apple Support.  *   (Link doesn’t always load)  

Get Support      -    Work through the screens to get a chat option. You may have to pick a slightly different problem.

Apple Support schedule phone call.   -

Apple on Twitter        

From the Apple Support article below. 

Without proof of your identity via security questions and other carefully selected criteria, Apple Support can't help you reset a password or perform any other actions on your account. These policies are audited and reviewed on a regular basis.

Security and your Apple ID - Apple Support.      *

I don't think you can change your birth date to make your account an adult account. You can only change the birth date of child account to any birth date below 13

That is stated in this article

Update the birth date associated with your Apple ID - Apple Support