You can show ID at a real world store and buy an age verification token. The token is good for exactly one user account on one website for one year. The website is responsible for ensuring no account sharing.
No need to store IDs online and it's still pretty hard for kids to access anything we don't want them to. Just like alcohol and tobacco there will be straw purchasers who re-sell to minors, and we accept that imperfection. We also punish people who re-sell or give alcohol to minors.