Every election I verify that my precinct is counted correctly. I'm just a regular citizen but I work as a volunteer election official (but you don't need to be that for just checking). There are a lot of people like me. If you don't trust any you can check as well. And everybody can do this – no university-level Math education needed.

To change the outcome of an paper ballot election you need to have thousands of thousands of people on your side and have everybody keep quite.