How do I change the age of an account that is a child's account without the parent account?

Ok in that case I suggest you to contact support directly and see if something can be done Mihai

https://support.xbox.com/contact-us

It is permanently suspended.

Hi,Mihai ! I'm Luis, a fellow Xbox Gamer . Thanks for reaching us out here.

Unfortunately you can not do that

You need to wait until the account "turns" into an adult by itself according to the initial birth date. This is to avoid actual childs changing the birth date.

Have you tried with the account recovery form?

https://account.live.com/acsr

Depends if the account in question is adult (18+ of age) or a child account. If that is a child account only the parental account can change privacy settings.

How to change a birthdate on a Microsoft account
Applies to: Microsoft account

For adult accounts (includes most people, in most regions)

1. Sign in to Your info on the Microsoft account website.
2. Select Edit date of birth.
3. Change your birthdate, and select Save.

For child accounts, or parents changing a child's birthdate
If your child is above the statutory age (13 in most regions), they’ll need to sign in and update their birthdate using the steps for an adult account. If they're below that age, you can do it for them. Note: If their birthdate
incorrectly shows them over the statutory age, they need to update it as if it's their correct age by using the steps above for an adult account.

1. Using the parent's Microsoft account, sign in to your account on family.microsoft.com.
2. At the bottom of the Your family page, select Manage my child's profile info.
3. In the Manage permissions page of the child’s account that you want to change, at the right, select Edit this child's personal info and then follow the instructions.

For help with age verification, see Parental consent and Microsoft child accounts.