how to access an child account with forgotten password?

Because the account’s birth date makes it a child account, it cannot change its own date of birth and must always be managed through an adult Microsoft account.

There are two separate issues here:

1. The child account has the wrong birth date and is treated as underage.
2. The adult account that gave consent cannot be accessed because its details are unknown/incorrect.

From the available guidance:

• A child account cannot edit its own date of birth. Where the listed date of birth is below the statutory age, only the adult account that provided consent can change it.
• If the adult account that gave consent is not accessible and cannot be recovered, there is no supported way to bypass that consent or convert the child account to an adult account early. This is specifically to prevent children from bypassing Family Safety and age restrictions.
• In similar cases, the only supported path is either:
  • Recover the adult account that gave consent (using normal account recovery and security-info replacement flows), then sign in to the Family/child-management pages and edit the child’s personal info; or
  • Wait until the child account reaches the statutory adult age in the region, at which point restrictions and “child” status can change.

Given that the adult account “isn’t an account” when trying to sign in, the next step is to try full account recovery for that adult account:

1. Use the Sign-in Helper to check for any issues and guided recovery steps: Sign-in Helper.
2. If that does not help, use the account recovery form to attempt to regain access to the adult account, following the detailed guidance in “Help with the Microsoft account recovery form.”
3. If recovery of the adult account fails, the child account’s birth date cannot be changed and the account will remain a child account until it reaches adult age.

There is no supported method in the provided guidance to:

• Turn a child account into an adult account by changing its birth date from within the child account itself.
• Move the child account under a different adult account and change its birth date without the original consenting adult account.

References:

• How to change a birth date on a Microsoft account
• Troubleshooting Microsoft Family Safety
• Managing parental consent
• I can't sign in to my Microsoft account
• Help with the Microsoft account recovery form
• how to change date of birth child to adult - Microsoft Q&A