Most "Axx prefixes date to 1984. Call S&W Customer Service at 800-331-0852. They have computer records of most guns made since the alpha-numeric SNs began. Those records reflect the date the gun was "put-up", not ship date as the older manual records did.
Few guns were kept around for more than a couple of days after they were assembled and tested. Why put a popular gun on the shelf, when you could sell it instead?