This may or may not help with your particular issue, but I recommend using su -l git to open a login shell as the GitLab user, and then run commands without having to prefix with sudo. I’ve found this helps take care of environment issues, which may be what you’re running into, especially if you’re using rbenv or anything (you’re not, so I digress).
You said there wasn’t a git user; there won’t be a git user until you make one unless you’re using the omnibus package or something. How are you trying to do the install?