Don't forget teenagers can be extremely skilled technically. Plus they have a lot of time!

But you're on the right track.

I think of a solution like:

1. Browser does one-time age verification through 3rd party service, without disclosing any details about which sites you'll access.

2. Browser stores your age, signed by that service.

3. When a site requests it the browser passes that signed age over. The site simply has to check if it has a valid signature by a trusted authority's public key.

The browser could even use Palantir in this example - but they would never get any data about what users are accessing.