It can be done by using a pre-defined Geoserver Docker container.
Investing the time to learn Docker is really worthwhile as it allows you to stand up and replace your cloud Geoserver instances very quickly. Adding to the Dockerfile will also allow you configure Geoserver automatically with your workspaces, data sources and layers.
Yes, I've read up on this being possible, at least through the OpenGEO Suite which is offered by Boundless Geo which packages Geoserver as part of their stack. I came across this release from Boundless Geo that mentions GeoMesa's collaboration and efforts to provide geospatial analysis and leverage Geoserver for spatial processing on Google Cloud.
You could read up more here on the announcement
You need to install tomcat on it, then use tomcat to install Geoserver Web Archive.
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