It looks feasible to have Gitlab push to a mirror GCP Cloud Repository, which can then be used for Cloud Builder Build Triggers.

Seeing as Cloud Builder's github/bitbucket integration is basically a pull mirror, I doubt you would be losing much if anything by using Gitlab with it.

After you've set up your external repository, Cloud Source Repository creates a mirror of your repository. https://cloud.google.com/container-builder/docs/how-to/build-triggers#creating_a_build_trigger