Each polling station should have representatives from multiple parties as well as independent observers.
> how can a constituent know with absolute certainty that their vote was counted
The representative of your party plus independent observer said all votes at your polling station were counted. You know both those community members and know them to be generally honorable. Ergo your vote was counted.
> every voter in the system was legal
None of the observers at the polling station, or the station head claimed any illegal person voted.
> the final tally was authentic
The observers all signed as witnesses on the final tally.
This is not the "system. it is humans you know who are telling you what they saw. If you can't trust other humans at their word, democracy cannot fundamentally work.
You should trust political volunteers after you have seen their track record of being honest and truthful. (Though there is some default amount of trust the process gets because of the adversarial nature of volunteers with opposing biases checking the process).
This is along the same vein as
You should trust candidates for the seat after you have done your due diligence that they have honest and truthful, and will faithfully represent you in the legislature/administration.
as well as
You should trust civil servants to have done state activities justly and produced truthful records and reports of state activities after you have seen a record of them doing these things correctly over time.
Democracy with humans is built on a lot of trust in humans. We have to keep this in mind when arguing about these things.
You do not have to watch every district, every election, every time. But given that enough people do it, at least once, at least in their own district, then it is easy to see why the system as a whole is trustworthy.
> how can a constituent know with absolute certainty that their vote was counted
The representative of your party plus independent observer said all votes at your polling station were counted. You know both those community members and know them to be generally honorable. Ergo your vote was counted.
> every voter in the system was legal
None of the observers at the polling station, or the station head claimed any illegal person voted.
> the final tally was authentic
The observers all signed as witnesses on the final tally.
This is not the "system. it is humans you know who are telling you what they saw. If you can't trust other humans at their word, democracy cannot fundamentally work.