I'll configure my Jenkins build job to poll the Git repository and use Git pushes as the trigger for a new build.
Jenkins will connect to Git through the repository URL for Gogs, and all the actions to build, test, and deploy the solution will run as Docker containers. The Gogs server and the Docker Engine have different authentication models, but Jenkins supports many credential types. I can configure the build job to securely access the source repository and Docker on the host.