If bitcoin, there are bitcoin ATMs, not sure if these exist for other coins. Find such ATM and buy with cash. Wear a mask and sunglasses and a generic hoodie with the hood up.
Disclaimer: I never used these, only know that they exist.
I found a youtube video demonstrating the use of a bitcoing atm to deposit into a wallet, it did not show any ID or "take a photo of your face" requirements, just a simple deposit, perhaps times have changed?