It is very much possible with paper voting, or at least you can personally inspect every step of the way in the process for a small slice, and you can understand how others like you verify things in other slices.

Ultimately, you do need to rely on your co-citizens to help verify that the elections are valid (in a simple to verify system, i.e. paper voting), just like you need to rely on them to vote coherently and to abide by the results of the election.