My naive approach would be to start a new Git environment, push the whole project into the master branch and then continue to develop the project using Git as if it had been there all along.

That seems like a perfectly good approach. If you don't have the history of what you've done so far in any convenient form then you can't get that history into git. If you have some old versions but not tracked as any systematic series of versions then it's unlikely to be worthwhile converting that series of ad-hoc versions into a git history.

So probably the best thing is to just add all files that make up the current version of the project (excluding anything that needs to be kept secret) to a git repository and then use git to track changes from now on.

My naive approach would be to start a new Git environment, push the whole project into the master branch and then continue to develop the project using Git as if it had been there all along.

That seems like a perfectly good approach. If you don't have the history of what you've done so far in any convenient form then you can't get that history into Git. If you have some old versions, but not tracked as any systematic series of versions, then it's unlikely to be worthwhile converting that series of ad-hoc versions into a Git history.

So probably the best thing is to just add all files that make up the current version of the project (excluding anything that needs to be kept secret) to a Git repository and then use Git to track changes from now on.