Git on its own is terrible for large files, but with the git-lfs extension it becomes somewhat managable with team members not having to download and locally store the entire history of your repository. You do have to tell it which file types should be considered “large files” though, such as all .uasset files, .png files, etc. or simply all files if you do not care for diffing text files.
Git-lfs also supports file locking (even though I never tried it myself) and there are a number of free and open source locally hosted git servers such as GitLab, Gitea, or Gogs, just to name a few.