In google classroom, you can schedule assignments by date. Is it possible to use the API to automatically assign the next scheduled assignment once a student has marked the current assignment as complete?
The API doesn't seem to provide an easy way to do that.
If you look at the documentation for the Classroom API there is no out-of-box mechanism to track when a student assignment is "turned in". You'd likely have to code something yourself to poll the state of a submitted assignment for a given student and if the submission is flagged as "turned in" use the API to trigger the next assignment in the sequence. A viable approach but not exactly trivial to implement.
Ironically the API supports push notifications for roster changes. Maybe google will expand this someday to include tracking submission state. You should consider posting a feature request using Google's issue tracker - this will at least put this need on google's radar.