I have been in the same situation. My recomendation:
- Clone the database project using Visual STudio Git.
- Develop you T-SQL objects using SSMS and test them.
- When your T-SQL objects have passed testing
- Create a new branch using Visual Studio Git
- Change or Add T-SQL objects you developed on SSMS
- Commit them using "git commit -m"
- Push the changes using VS Git to the database project
- Create a pull request.
Basically, keep using SSMS to develop but when changes are ready, use Visual Studio Git to submit your changes to the database project source control.
Hope this helps.