Solution 1:

In order to work properly in GCE and interact with the execution environment, a guest OS should be pre-configured appropriately. Usually it is done by Google or Linux vendors in the process of preparing the system image.

Compute Engine > Doc > Guest environment > Supported operating systems

Compute Engine > Doc > Guest environment > The Linux guest environment

Since Alpine Linux is not listed among either the Public images provided by Google or the Community supported images, it is up-to-you how to prepare the Alpine Linux to run in GCE.

There is an instruction out there you can follow:

Setting up Alpine Linux in Google Cloud Platform ( GCP )