I went snooping around the internet, and found that there was this magical software called Nix, which would let you have a package manager without root! The Linux computers in the lab didn't have root, but they did have GCC. I started learning all about build systems (mainly that you could specify a custom --prefix and essentially create your own filesystem within your filesystem), and got to work compiling Nix (or, i think, GUIX) from source. It's actually a fantastic amount of work to go from GCC all the way to a functional GUIX, even with access to every source tarball on the Internet
Eventually some admin emailed me about this project and I stopped working on making it happen shortly after, but it was such a formative experience in my tech life that I always think back fondly on it when Nix pops up.