Realistically, the options on Linux are the uv way, the pyenv way (download and compile on demand, making sure users have compile-time dependencies installed as part of installing your tool), and letting users download and compile it themself (which is actually very easy for Python, at least on my distro). Compiling Python is not especially fast (around a full minute on my 4-core, 10-year-old machine), although I've experienced much worse in my lifetime. Maybe you can get alternate python versions directly from your distro or a PPA, but not in a way that a cross-distro tool can feasibly automate.
On Windows the only realistic option is the official installer.
But overall, computer literacy is really on the decline these days. Nowadays before you can teach programming in any traditional sense, you may have to teach the concept of a file system, then a command line...
You only have to do it once per version with this approach. Then you can create venvs from that base, and it's basically instantaneous if you do it `--without-pip`.