I was thinking if it make sense to use Firebase for a non real-time app. Is there some other service that allows you to store a json and retrieve it as a RESTful API?
Sure, just use the Firebase REST API https://www.firebase.com/docs/rest/api
As an alternative you may want to check out Realtime Cloud Storage (the company I work for). It's powered by AWS DynamoDB and has a REST API that you can easily use to store and retrieve json data.
REST API: http://storage-public.realtime.co/documentation/rest/1.0.0/realtime.storage.operations.html