You will need to take a different approach to achieve this type of functionality. I have also had a look at the documentation, and I cannot see anything in the API Cloud Run methods that meet your requirements.
However, if you implement a CI pipeline to GitHub, you can test and deploy to Cloud Run automatically. Utilising a Code Repository will ensure that your code is always version-controlled and provide a workflow more suited to developers. Have a look at this tutorial and the GitHub API for more information.