It is doable, i think. Consider:

You go to your local library. They verify you’re above the age limit (like they do at supermarkets when you try to buy alcohol: either look you in the face and recognize you’re clearly old enough, or have to show them some kind of id, details vary.)

You pick a code (put your hand in a box and draw a piece of paper at random). Nobody knows what code you picked except you. If lots of people do this at the same time, it’s impossible to accurately map codes to people’s identity.

You scan the code (like QR code) with your social media app that you use, and it associates the code with your account. Now everybody knows you have a valid code associated to your account, but nobody knows your identity.

The code could work something like a cryptographic signature, where you can show that you have a valid code without actually revealing the code, so others can’t simply copy it. That’s a technical detail that you need to leave to the programmers to accurately understand.