I never used Mint but if it is using apt, then it has to be able to find snapd unless I’m missing something. Have you confirmed you have the options ticked to accept software from given ppas?
I don’t know where these are in Mint but in Ubuntu it’s under Software Sources in the Software & Updates settings menu.
I recently noticed some colleagues were having issues installing software in a container right after installing because they weren’t updating first. This is a long shot but if that’s a brand new installation, updating first is always important. Nevertheless,
sudo apt update can return important errors. Can you ensure this command gives no errors?
Sorry if these sound very basic but I don’t know how well accustomed to Linux you are so I have to try everything