I looked into this, apparently it is a legal requirement in the US for contacts.
That said, for normal eyeglasses, there are many sites that offer eyeglasses without proof of prescription. I've been buying eyeglasses from Zenni Optical for almost a decade for my whole family. Most recently in 2021. I have never once even been asked for proof of prescription, I just punch in my numbers and hit order.
Some online shops make an effort to validate vision prescriptions, others do not. My most recent contact order was through Lens Direct, who did not validate. 12 years ago I gave an incorrect phone number for the optometrist. They tried to call but did not connect, and sent me an email: 'we're going to send your contacts anyways...'
The optometrist I went to recently put me in the strongest prescription I'd ever had. Instead of using that prescription, I ordered contacts using the prescription of the glasses that I thought were fine.
There's two numbers on the contacts... diameter of the pupil (doesn't matter for most people I think) and an angle (Edit: 'Base Curve'. The third number is the power of the contact, aka 'sphere'. Glasses prescriptions have power and astigmatism, but don't have diameter or base curve). I got these off my prescription. If you don't already know how to use contacts it's important to get instructions and a followup. I read of a guy who didn't know he had to take the contacts out at night - the contacts had started to grow into his eyes?
(Edit: you can get a set of "trial lenses" from Ebay if you want to try to come up with your own prescription, or to try out your prescription before buying glasses.)
But please link me to a US site where I can legally buy contacts without providing proof of prescription, if there is one!