The best way to collect documentation/files from students is to use a Canvas tool like Assignments (confidential submissions) or Discussions (public submissions). You could also ask students to send you files via the Messages (Inbox), but that lacks the direct connection to course activities like the other tools. If you use an Assignment, submitted files can be downloaded all at ones with the students' names prepended to the filenames.
Unfortunately Google Drive does not offer a dropbox-like function where a folder can be set up to allow other users to upload a file without the ability to remove files uploaded by others. And you would either have to make the folder open to anyone with the link or know all of your students' Google user accounts so you could share the folder only with those users. I would love to know what Google Drive offers that would be worth losing confidence in the integrity of items submitted to that folder.
