The terms you're looking for are Linux Live USB, or netboot. Both often make use of local RAM disks.
One way is to burn a CD/DVD live image that has your configs added and configure it to mount a mergefs(iirc) on top of the read-only /home so all writes go to /tmp/merge.
But past that, I don't see how you can do anything since installing programs would require storage.
Most live linux has support for saving stuff to the flash drive. It runs slowly but works.