You can check any report's status that you've created via API using the endpoint /publisher/export/get. More information about its parameters is available here.
Ideally, you should wait until this call returns the status completed and only after that try to download the report via the endpoint publisher/export/download.
Otherwise, you'll receive an error message Export not completed yet.
A sample Sandbox API request for downloading a report can be found below:
https://sandbox.piano.io/api/v3/publisher/export/download?aid=[AID]&api_token=[api_token]&export_id=123ABCXYZ