So, the first thing to check is for simple REST APIs that you can curl. If I recall correctly, GAE is tricky because it takes more than 1 API call.
Next, check for a CLI or script library. I see Google provides an SDK that might work: https://cloud.google.com/appengine/downloads#Google_App_Engi...
In that case, we have to pull the library into an appropriate image. For example, here's how the Amazon folks solved for S3: https://bitbucket.org/awslabs/amazon-s3-bitbucket-pipelines-...
I won't have time to look at GAE more closely until next week, but hit me up on Twitter if you want to DM me: @devpartisan