Photo ID works great, is preferred. If you've already been entered into the State computer, they can ask people questions to verify their identity in the case of lost ID.
Yes you normally have to have id but if you have those two forms of id they might be able to help you get one. Or put you through their system another way.
I'm not sure, you might be able to do birth certificate + ss card and maybe some mail in your name at an address or school photo ID to supplement. Call them and ask during business hours.
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