I think the most straigthforward solution for you would be to boot the live ISO installer in a virtual machine, and then connect the USB device to it and then install. This is mostly guaranteed to work, since it is already using the actual ISO.
Alternatively, the program that most Linux distro's use to install nowadays is called calamares. And yes, you can install it on a non-live system.
sudo apt install calamares calamares-settings-debian
This might be easier, but it also might be harder, if say, the installer is not preconfigured with the various settings the live ISO comes with.