Best practices for automating Looker production deployments from GitHub production?

What is the best practice for automating deployments to our Looker production environment? Currently, after pushing updates to our production branch in GitHub, we have to manually click “Deploy to Production” in Looker to see the changes.

Is it possible to automate this final deployment step, or is the manual click always required?

Would like to automate this step so that a push to the production branch automatically deploys the changes. What is the recommended way to set this up?

We use webhook deploy outlined in this doc Configuring the webhook deploy secret  |  Looker  |  Google Cloud