It probably won't be too long before someone creates a tool to create fake Git/Github entries to "prove" a document was written by a human after it was actually ChatGPT-generated.
I'm probably just not smart enough but I can't figure out how to truly prove your (human) authorship. To some extent though I'm also not sure how much it matters. If the science is sound, the text is well written, and the paper is well presented, why do I care who wrote the text? I didn't handwrite the graphs or the tables of data, that was a script. Nor did I typeset every letter, that was LaTeX. The text isn't even any different in nature, like the difference between an original oil painting and a print of the same. It's ultimately just a means to communicate ideas from my mind to yours. Perhaps it is ethical to disclose the use of generative AI, but I'm not convinced that would be any better in the minds of the reviewers in question here. I just don't see a substantiative difference if the end product ultimately is high quality.
For what it's worth, I wasn't a great student (good at learning, yes, good at going through the motions to get good grades, not so much) and despite what some might call an academic approach to most problems I'm not really a fan of academia itself. There's a lot of stuffy old practices, like p-value being the metric for so many things despite the knowledge that it can be "hacked", and weird, unknowable financial or political motives that you'll never be privy to, which in my opinion compromise the integrity of the work more than use of generative AI does while also being harder to detect. I'm certainly not the first to point these issues and I won't be the one to solve it. I do wonder though if the whole thing is kinda broken, ChatGPT or not.
Edit. Btw, you can use Git with Word's docx-format out of the box. Docx is a zip folder with XML inside; git-diff will show text changes. Further, there's git-merge-driver for merging various file formats (https://github.com/Praqma/git-merge-driver).
The paranoia we are seeing now will slowly fade. It doesn't make sense to adopt extreme measures, especially since the truthiness of any claim as to creative originality becomes more dubious with every day.
Even if you hand-wrote and mailed a copy of your manuscripts one page at a time to the US Copyright Office, that would not suffice, since from the moment ChatGPT was made public, you could have been using it, then transfering your thoughts to paper.
Just live your life.