Consider building with Cloud Build

Today, we build locally in Cloud Shell and then push to GCR.

It is not clear if this is fastest than building remotely in Cloud Build, have you performed benchmarks?
It also seems that the push stage takes a lot of time in Cloud Shell, while it is likely faster in Cloud Build.

Maybe it's a good opportunity to implement both, collect metrics and A/B test.

Note that Cloud Build can be used for Docker builds, but also for buildpack based builds with a custom cloudbuild.yaml