How should I deploy a .NET Core app on Linux with Google Cloud Platform?

Deploy to Compute Engine, which "lets you create and manage virtual machine instances. It supports a range of... Linux distributions, plus sizing, and configuration options."

Configuration management tools let you automate deployments.

This is a push-based deployment, in which "the deployment artifact—a zip file, a NuGet package, or another artifact—is initially available only to a deployment server."