many countries already have a working system mostly integrated, so yes, i would say it is possible.

the government should issue physical tokens that are sold wherever you can buy booze or smokes. when you login to a service that needs age verification, you type in the code from your age token.

its pretty cheap, its low-tech, we are already accepting of showing id to a store clerk privacy-wise, we generally trust the enforcement mechanisms around smoking/drinking already, it would be easy to expand existing laws to accommodate selling them/punishing misuse.