That weird. If your configuration file really doesn't exist, then executing git config --global --list should give you the location is it expected to be. You should check if permissions to that directory are sufficient for git to write to that file...
You can also execute git config --global --edit to edit the file directly.
If you want to change your config file path, you can do so by creating an environment variable called home, and pointing it to your desired location.
See Git Config Documentation for additional information