I haven't actually tried it out yet (about to) , but just by reading the instructions on deploying, it looks like you stage your code in a GCS bucket or on a Git repository (Google Cloud Source), so I think your local data would refer to any files in that bucket/repository along with your code.

*edit note: looks like you can definitely add more files via the package.json and import them as node modules, but I wouldn't rely on reading and writing from the file system.

As for persistency, if it's just Javascript code you can install node modules to accomplish what you want including talking to those cloud APIs. Unfortunately Bigtable might be the exception since I'm not sure if there's a good nodejs client yet (Bigtable only supports gRPC, not REST), but you could use Cloud Datastore instead.

Firebase will also be a very popular choice for persistence. Cloud Functions naturally complements Firebase to complete Backend-as-a-Service. The hope of Firebase is you don't need a server at all, but sometimes you have logic that really doesn't belong on a client (background jobs, "master" logic). Cloud Functions can fill in those gaps.

Firebase: https://www.firebase.com/

hand-rolled clients nodejs clients for google cloud apis: https://github.com/GoogleCloudPlatform/gcloud-node

auto-generated nodejs clients for google apis: https://github.com/google/google-api-nodejs-client

disclosure: work for GCP