To start the process of temporary residency in Paraguay requires 1 visit in Asuncion for 3 working days.
The process normally takes 1 business day but it is good to have an extra “time buffer”.
It is also important to avoid public holidays: https://hackinglives.com/knowledge/paraguay/national-holidays-2024/
If you are not in a rush you can explore the city a bit more: https://hackinglives.substack.com/p/explore-asuncion-your-complete-guide