If the student cannot begin an activity you've assigned to them and seems to be stuck looping between the "Begin with Google" page that TeacherMade presents, and the Google sign-in process, it's possible that their devices is blocking what is know as "third party cookies." Third party cookies are just web cookies, like many applications require, but fall under stricter security restrictions. Sometimes a student's device is setup to block third party cookies which may be causing this loop.

To allow third party cookies on the student's device, read this article: How To Allow Third Party Cookies