Do you have access to the server? If yes, you can connect to the SQL database directly and query the mdl_user (from memory) table. You would need to be able to login on the command line and then login to the (probably MySQL) server from the command line. If you don't know what that means or how to do it, then probably you need to be liaising with whomever are the sys admins.
(Archived forum) Moodle research
How can we get Moodle students registration data?
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