I want to install Debian directly onto my USB drive. Is there an easy way to do this directly without having to reboot to run the installer?
Copy a live cd iso using dd.
This doesn’t really install it, though, you can’t update or permanently edit and config, set up users, or anything like that. I would guess OP wants something more like booting the ISO in a VM, allocating a thumb drive to that VM, and then installing a full system to it with a boot loader.