I worked there twenty years ago, so things may have changed. But back then, you had to take a civil service exam.

They’d do them 3 or 4 times a year, usually on a Saturday at the nearest big city. On the exam, you demonstrate your ability to read house numbers, understand traffic laws, and in general not be a complete idiot. Then you pick your top three post offices you’d want to work out of.

When one of those offices has an opening (which can take months), they interview candidates starting with the highest-scoring people who took the exam and working their way down until the local manager finds a good fit.