I lost about three weeks because I didn't realise one registration had to happen before everything else could. What's the sneaky appointment or step that people don't know is on the critical path?
Address registration. In a lot of places it's the key that unlocks everything — bank, tax number, health system — and until it's done you're stuck. Do it the first week.
For me it was the domino: tax number gates the bank, the bank gates the flat. Once I saw the chain I stopped doing things in the wrong order and everything sped up.
Book appointments the day you arrive — waitlists for the popular offices are weeks long. The checklist in the country guide lays out the order things need to happen in; that saved me from exactly this.
Registering with the health system. I assumed it was automatic. It very much was not, and I found out at a pharmacy counter.
The "domino" framing is perfect — that's exactly the three weeks I lost. Pinning this for the next arrival who asks.