It should start normally through the itch.io launcher if you are using that?
It is built for and tested on Ubuntu 22.04, but it should work on any distro a glibc of 2.35 or newer (newer Ubuntus, Debian 12, Arch should all be fine)
Unfortunately as we are still in development we only support recent versions. I have added a note about requirements on the itch page. We'll review these later in development to include as many distros as possible, but as we don't have a 32 bit machine to test with, it is unlikely we'll ever build for that.