Answer
For some categories of residencia, the application can be started while in Uruguay after entering as a tourist. Tourist status itself does not guarantee eligibility for the chosen procedure: before applying, check the category, permitted duration of stay and DNM requirements.
Before the trip, it is worth collecting certificates, official records, apostilles, translations and proof of income, but do not state a false purpose at the border. Preparing for a future application does not mean the status process has already begun until the application is accepted by the competent authority.
After entry, keep your entry stamp or electronic confirmation of crossing the border. It may be needed for your application. Also keep an eye on the permitted tourist stay: having an appointment or waiting for a date does not always automatically extend the permitted stay.