Does make files ever actually work that way? In my experience they always require you to install a bunch of packages for libraries which usually only tells you the package names for ubuntu so you have to hunt down what the package is called on your distro or if that version of the package is even in the repos.
If you write them yourself they certainly can. For small projects, you can leave everything explicit and it works great.
Can you break down your problem into a bunch of rules of the form “To produce this file, I need to run these shell commands, which read those other files over there as input”? If so, Make can take care of figuring out which steps actually need to be run.