You mention that the code is constantly updated and must be shared with colleagues.

Are you the only person modifying the code? Or do your colleagues modify it, too?

If the latter, distributed version control is why git was created.

Git isn’t the only way — certainly distributed projects existed before it. But you’re going to need to use version control and I don’t think you’re going to have an easier time convincing or teaching hesitant colleagues mercurial or svn instead.

For reference, I am also a (non-software) engineer working with code. We have an internal GitLab instance. There were definitely growing pains getting folks to use it. But it’s certainly been better than asking Joe for his version of this code and Bill for his version of that code and getting them to play nicely together. It helps to have your leadership on board. So a department chair in your case, perhaps?