I have a spring boot application, angular front end app, couchbase, and redis. They are all defined in a docker compose yaml file. I can make the application up and running locally. Is there a way to use docker compose tools/commands to do the same in google cloud or digital ocean?
If you don't want/need platform-specific integrations and transforming your services to a cloud I guess GCP Compute Engine is for you -- it's like a usual virtual machine that you can start, SSH to it and have all privileges to install and run software the same way you did it on your dev machine.
If you want to avoid Kubernetes, then the simplest of the GCP options for a docker container is probably their Container-optimized VM images?
That lets you put the parameters to your
docker run ... command in the VM config as per https://cloud.google.com/compute/docs/containers/deploying-containers#gcloud
This assumes you are able to publish your image to a repo that is accessible to your GCP compute VMs.
I don't know about Google Cloud but yes on Digital Ocean, I do it all the time! Just make sure you have Docker Compose installed on the droplet and then run the commands the same as you do locally.