Any paper voting system that is not entirely open for inspection is inherently open to alteration. Software systems are hardly unique in this respect.

https://www.youtube.com/watch?v=sJfj9ySYg0Q

Electronic systems make manipulation data on a small scale harder but on a large scale easier. A large scale attempt to alter paper ballots is far harder to keep under wraps just because of there being more people involved.

The difference is that making paper voting systems entirely open for inspection is inherently much easier than doing the same for an electronic voting system. Especially for non-experts in engineering and cryptography, that is, like, 99.9% of the population.

Apart from mass civilian surveillance combined with breaking in and entering on a large scale, how do users inspect a paper system?

Observation works pretty good.

You can be a poll inspector, a poll judge, a poll observer, watch the central count, attend the public certification hearings.

Different jurisdictions have different rules, so YMMV.

But the basic ideas are a) Australian ballot system b) verify the physical chain of custody c) private voting, public counting.

Happy hunting.

By having representatives of their own party being present in every single place where votes are counted. At least, that's how it works here in Italy.