You can see the date a learner enrolled in a course in the Learner Progress Report. Select Download full report (CSV) to download the report in CSV format.
The 'enrollment_date' column indicates the date in which the learner enrolled in the course. The 'unenrollment_end_within_date' column indicates the date by which the learner must unenroll for your enterprise to receive a refund on the enrollment. This date is traditionally 14 days from the enrollment date or the course start date, whichever is later.
For more information about the data that is included in the learner progress report, see the Working With Learner Data article (https://business-support.edx.org/hc/en-us/articles/360005425093-Working-with-learner-data).