Why not bind it to the phone itself? The phone (or a phone app) would verify you're an adult, and beyond that the website would know nothing but that 1 bit of information.
This creates a grey zone where a 16yo could buy their own device and set themselves as an adult but grey zones like this aren't really a bad thing.
There's also no penalty for lying. If an adult wants a child to have an adult account, they can.