Yes, kind of. In a similar way that we can currently authenticate with OpenID. Basically something like a passkey could be issued by your government that would let you prove your (pseudonymous) identity (and thus age range) through their API to a website.
This wouldn’t allow for anonymous browsing, since the website would have to identify you, but it could allow for pseudonymous browsing, since the website’s identification of you could be just an ID number that is specific to them. They already track you with cookies, so it wouldn’t be any worse than we have now, except that it’s more unnecessary bureaucracy.