Do you not have a record of voters?
In backward NZ it is compulsory to enrol at I think 18, this role is updated with your current address just before an election. [every 4 years, unless there is a special election].
Voting is not compulsory, before getting the voting paper your name and address is verified and the, [at the moment paper book] is marked.
After the election, each name is checked to make sure nobody voted twice.
With the number of people in the US, the paper system wouldn't work, but a computer would laugh at the job, and it would be instant.
Not listed, no vote.