For a lot of courses or just one? Just one, run the student history in the course. It will show you when they actually started.
Your first question: That might be when they enroled...not necessarily started.
Your second: So, prefix_course_completions includes a start time...but it doesn't seem to have much relevance. I looked at one user and their course...they enroled Oct 9, 2017. The start time was Feb 26, 2018. They had no documented activity in that course for that day. My site logs don't go back over a year, so I can't backtrack for this user so I looked at a more recent one: time started is Dec 17, 2019...but so is the time completed. The course has one required activity, when you complete it, you're done. So it looks to me like completions start time is when the first course completion requirement is complete, not when they actually started the course. I picked another user, randomly, and this theory was borne out--first activity completion registered at 7:25 and last completed activity at 8:50--she enrolled at 7:13 and started her first activity (SCORM
) at 7:14. You'll also notice the date enrolled goes to 0 when the time started field gets filled in--when time_enrolled has a date stamp, time_started is 0. As soon as time_started gets a date stamp, time_enrolled goes to 0.
You're probably better off looking at logs for start time, or user reports. Is this really that important?