Continuous age verification isn't possible, so you'll have to store some sort of proof of age somewhere, and that proof will always be sharable.

Let's say Facebook has verified my age somehow. I could share my Facebook login credentials, or the token that their authorization server sends back in response. You can create some hurdles to doing that, like requiring a second factor, but I can just share that too.

You might as well go down the route of accepting that possibility. These systems are never going to hold up in the face of a determined enough teenager.