To see the date a job was originally created and published, visit the Activity Stream and select the Published filter. You will see in grey font when it was published. To view the exact date and time the action happened, hover your cursor over the timestamp.
Note: Details about Archived jobs are not available in the Activity Stream.
In addition to the above option, you can visit the Activity log report. The Activity log report will contain publishing details for Archived jobs.
Just select the job from the filter on the left and set the date filter to all time. Download the report in a CSV and then filter externally (in Excel) by the activity "Published job".