On the client: The typical parental controls situation with a blocklist. Responsible adult sites could send an HTTP header like X-Adult-Content or something to ensure they would be blocked by clients with the controls on. This could be enforced by regulation, with devices for children required to respect that header in addition to shipping with a blocklist. This couldn't be bypassed with something like a VPN (which you probably couldn't install with parental controls on anyway), because it would be baked into the client.
In the network: Similar blocklist style situation - this already exists to a certain extent in some countries. Mobile phone providers and ISPs would be required to block adult content (via dns or similar) by default, with a toggle to switch it off available to the adult account owner. We already block illegal content this way.
On the server side: This requires adult websites to be cooperative, which they will only be if they care about the jurisdiction in question. This potentially pushes kids/others to access sketchier sites which wouldn't be blocked.
I am strongly for pushing this down the stack to the client. I don't have kids, but I'm pretty sure iOS and Android as well as MacOS and Windows all have robust parental control systems. I'm sure people use them, and we can safely encourage people to use them more. If they aren't on by default already for children, they could be.
Short of biometric verification with presence detection I don't see how it's possible to do remote age verification in a good enough way that you couldn't just use an adult's credit card or device to bypass it.
Anyone who knows anything about tech knows this is just a wedge issue, and people aren't interested in solutions to the actual problem of kids accessing inappropriate material, only soundbites.