You can see when a course was published (and by whom) by going to Admin Tools and then click the "Logging" tab. Select "Course Activity" from the drop-down. Put the Course ID (from the course URL) in the "Course ID" field and click Find. You will see a list of events when this course was changed. One of the line items will be "Published" and will include the date, time, and user who performed this change.
More info can be found in this guide. How do I view course activity for an account?
I have to say this information was (nearly) impossible to search for. I kept searching for publish date or something like that. Thanks to Ben Nelson from support who helped me find this. Thought I'd post it here because this topic kept coming up in my searches.