You can get the month and day by sorting a search result with the item among the results by "Time: Newly listed" (you have to have the "Time remaining" display enabled from the Customize popup accessed from the dropdown menu at the top right of the results to the right of the Sort dropdown). To figure out the year make sure you have a few dozen other results and scroll down from the top, counting the years whenever the dates go from January to December until you reach the target item.
