hey @bb2j3z, to expand on what @madikarizma said, it is indeed possible to download your generated deploy from netlify (i.e the stuff on the server that the visitor sees)
If you JUST have a static site with html/js/css/images/whatever, then i suppose you could download that (if you have access to the UI, which it seems like you do) and make a new repo, and then push that to github, and then switch your netlify config to use that repo, and then work from it. That is possible. Here’s how you download a deploy:
But, if your site uses anything that was generated in a build step (if it was built using a static site generator, like, hugo or anything else) then you won’t have access to the raw source files, as these are not included in your downloadable deploy. So, you wouldn’t be able to edit any of the original files and then build a new edited site. Does that make sense?
I’m not sure what your best way forward is - unless you have significant obstacles to getting control over the original repo, your best bet (and definitely the most consistent and technically easiest) would be to find a way to take possession of that original repo and just work with that.