This is a basic problem that has perplexed me for a while. On a machine running Ubuntu, is it possible to mount a new disk, run the Ubuntu installer the same as you would from a live CD and install on that new disk? I haven't figured out how to find the installer program(s) or what would prevent me from doing so. It sure would aid in deployment of the rare single machines if I could do a net install from the machine running my local mirror!
SnapOverflow
Four of the main features of Live installers are:
You specifically don't seem need #1 and #2 since you're already booted into a working system. You are sacrificing #4, which matters a lot to people who are surprised when their hardware doesn't work.
Look into dd-able images of Ubuntu Base:
Warning: Ubuntu base is not intended for beginners nor the unskilled. If the link above isn't enough information to get your Ubuntu Base system up and running, then it's perhaps not right for you; stick to the normal installers.
There are some other dd-able images, but they are for specific use cases like unusual architectures or pre-release testing. There is no dd-able AMD64 Focal Server image, for example.