Git is used by a lot of developers to keep track of their changes and to collaborate on projects. While the source code is typically hosted on a central server (Github, Gitlab, etc...), this server is generally not used for more advanced workflows.
Because most of the tasks you perform on a repository are very descriptive, you can use them to trigger build and deployment events. Pushing code to the server could trigger a deploy to the testing server, pushing a tag to the server could trigger a deploy to production, and so on! If you use semantic versioning, you can even target more specific deployment servers.
Git is already part of your development workflow, start using it as part of your deployment workflow: GitOps.