That's wishful thinking. The site would log that they sent you to verify your ID with your IP and a timestamp. The proxy server would get your identity with your IP and timestamp. Those two can can be linked. The government would know exactly who you are while also knowing where you came from and when.

Either the government would monitor the proxy or they'd just be running the proxy themselves or forcibly taking it over Room 641A style to log everything going in and out.

There is zero way to verify your identity to a website without trusting some third party with that information. There's no one in the US who is trustworthy enough or immune from being controlled by the US government so you'll always be vulnerable to having your identify exposed and it being used against you.

The best suggestion I've heard so far was scratch off cards that could be purchased anywhere in person, with cash, after presenting ID. The ID isn't logged or scanned, just manually checked by the wage slave at the counter. Even that isn't without challenges though since the cards would have codes that would likely be traceable to batches and where they were distributed to/purchased from which means that information can be checked against surveillance/facial ID/flock cameras to find out who bought them, and they can also be resold/shared online/exchanged/stolen/generated/given to others which means they won't be very effective at identifying individuals or keeping kids from seeing adult content.

The truth is that the entire point of these age verification laws is deanonymization, censorship, and control. Any theoretical scheme we might come up with that wouldn't allow for abuses will never be implemented for that reason.