In practice you don't convince Rust that everything is right. You let it prove that most of the code is right and you promise it (via unsafe) that the rest is. Ideally these unsafe blocks would be carefully documented, reviewed and ideally enclosed in small modules that makes correctness easier to ascertain.

Rust is no panacea, but in my experience it is far easier to write memory safe code when the risky bits are discouraged and explicitly highlighted rather than every line of code being a possible risk. Humans are pretty bad at reviewing 100 lines of boring looking code (especially if this is one of dozens of patches this week) but much better (although by no means excellent at) reviewing 5 2-line unsafe blocks amongst 90 other lines of code.