Ah, that would put a bit of complication into things. If you want to actually accomplish this though, you should largely start with the same steps as a standard system install, using a second USB flash drive to write the distro onto the external SSD, leaving enough space to build the rest of the partitions you need.
I’ve actually tried to install Fedora on an USB SSD to play around with it. But somehow the installer just refused to select the second USB drive as an installation target. I looked for quite some time but couldn’t find a way to do it. I ended up trying to install it manually like Arch (for fun), but never got a bootable system 😅 I was able to install Arch and NixOS on the same drive without issue.
I’m actually not sure how OP could achieve something close to what they’re looking for… A regular installation certainly seems like the right choice, but that may require using an internal drive.