Welcome to the forum, I see this is your 1st post. I don't know how much you've read this forum before but this may be your 'rude awakening' that we've all experienced about the disparity between when Smiths were produced and when they were shipped/sold.
The disparity has many reasons but is mainly influenced by market demand and what order completed guns went into the inventory safe versus what order they came out (usually reverse order).
When guns were produced can not be verified from the records, only detective work about the guns features and evolutionary changes can help get us close. The shipping date of course can be verified from the shipping records by request to S&W. The provided information is very helpful in verifying the originality of the gun and some provenance as to where it was shipped and when. Also as Glowe has provided, confirmed shipping dates in the database of same model guns with near serial numbers to yours can give you a possible shipping period.
However, I also find it very enligtening, to try and determine when a gun was actually produced in the evolution of Smith revolvers. The number of screws, roll marking placements and styles, thumbpiece and ejector rod styles, details of the stocks and medallion monograms, etc., all play a roll in this detective work and add to the interest of each new find. Production periods can align more with serial numerical sequence, but not always and it's far from being a hard and fast rule!