1. Commit the entire production codebase to git and push it to a host (GitHub would be easiest here)
2. Set up a cron that runs once every ten minutes and commits ALL changes (with a dummy commit message) and pushes the result
Now you have a repo that's capturing changes. If someone messes up you have a chance to recover. You can also keep track of what changes are being applied using the commit log.
You can put this in place without anyone having to change their current processes.
Obviously you should aim to get them to use git properly, with proper commit messages - and eventually with production deploys happening from your git repository rather then people editing files in production!
But you can get a lot of value straight away from using this trick.
It's basically a form of git scraping: https://simonwillison.net/2020/Oct/9/git-scraping/