Here is a list of allowed document for a similar problem, for employment. Note that it categorizes the possibilities as ID, citizenship, and work authorization, and you may need one each from multiple groups. For example you might use a drivers license as ID and a certified birth certificate as proof of citizenship
It’s not quite the same since this allows identifying as from another country and with a valid work authorization, which do not apply to voting, but very similar
Obviously I’m not saying this is appropriate to mandate for voting but if we were, this is a well thought out answer to that sort of question.
It doesn’t address the voter suppression concern though