How to get your first ID in Uruguay?

TL;DR:

1. Apply for permanent residence on this page: https://www.gub.uy/tramites/residencia-legal-permanente. To start the process, you'll need your passport.
2. Translate your passport into Spanish with a public translator: https://www.colegiotraductores.org.uy/
3. Apply for an ID here: https://www.gub.uy/tramites/cedula-identidad-primera-vez-personas-extranjeras-residencia-tramite-legal-definitiva-definitiva-mercosur. For this stage, you'll need your passport and its translation into Spanish.

Eventually, you'll also need to provide a health card from a local hospital (around 1,000 Uruguayan pesos), a translated background-check certificate from all countries where you've lived for more than 6 months in the last 5 years, as well as from your country of origin, and an income certificate from a local accountant. These documents are not required from the start - you'll have up to two years to gather them while your permanent residence request is being processed.