We use Git with LFS for our games-orientated projects, including some pretty massive projects, and have found it works really well.

We previously used SVN for similar projects, and made the switch to Git once LFS made it a feasible choice for projects with lots of large binary assets (games), and honestly never looked back, it's massively improved our workflow.

git lfs plugin should help with that one. IIRC Godot's editor has some support for creation of git repositories

https://git-lfs.github.com/

Smallish indie projects get by with git and or git lfs. git isn't really designed for binary assets and large games with terabytes of source assets usually don't use git. git's distributed nature is also an issue for non-mergable binary assets. The most common tool version control for bigger teams is perforce. It's significantly faster than git for binary files and it helps manage 2 or more people trying it edit the same binary file. There maybe be other bolt on solutions for that for git that I'm unaware of to help with that.

Your intuition is correct. git alone isn't going to cut it for the assets.