without having to reboot to run the installer?

I’m not sure that I understand what you mean. Are you saying that you want to be able to load the OS without having to reboot your computer? Or are you saying that you just don’t want to have to click the equivalent of “try the OS” when booting a live USB? If it’s the latter, you should be able to just select the flash drive as the install point (though, tbc, I have never tried this, but I don’t see why it wouldn’t work) (I think you’d need 2 USBs, though — you’d need 1 to be the installer source, and one to be the install point — I don’t think theres any installer that can run as a desktop application. Though, if it’s Arch Linux, you might actually be able to call pacstrap from the host OS — I’ve never tried this after having already installed the OS). There’s even OS’s that are specifically designed to be ephemeral on hardware in this way — eg Tails OS.