How to Resolve Activation Lock Issue After Deleting Child's Apple ID?

I created an Apple ID for my child as part of Family Sharing and used it on their iPhone. Later, I deleted that Apple ID but forgot to sign it out from the iPhone before deletion. Now, when I try to sign out from the device, it shows a message saying, "Your Apple ID is not valid or supported."

I still remember the password, but since the Apple ID no longer exists, I can't use it to sign out or remove Activation Lock. This has left the device unusable.

Has anyone faced a similar issue, and how can I fix this? Any help would be greatly appreciated!