Import your pet: microchip, valid rabies vaccination (given at least 21 days before travel), and — arriving from a non-EU country like the US — an EU animal health certificate issued by an authorised vet within 10 days of entry

The title is the checklist: microchip first, rabies vaccination given at least the stated days before travel, and — from a non-EU country — the EU animal health certificate issued by an authorised vet inside the title's tight window before entry. That last window does the scheduling for you: the vet visit lands in your final pre-flight days, so book it when you book the flights.