Please let me know if there is already an accepted way to do this.
Early in the install process, you’d have a field to type a hostname of a local machine that you’d like to install like. The installer would download an “Install facts” file and install the new machine like the model machine.
The “install facts” file is created at install time. it contains things like timezone, language, percentage of disk space for each partition (to handle disk space of differing sizes) Optional files selected, username/password for root and for first user - anything needed to make the install a two click operation.
Note that this would be a full new install - not a clone of a machine that has been in use for a while.
This is not really a highly requested feature, so I’m not sure that it exists. You’d probably be better off writing a simple cloud-init config and using that.