The gun you have was made under a WW1 US military contract. The US entered WW1 in April 1917 and the fighting ended 11-11-1918. If you don't have any of the S&W history books, you might try to look up online to see when the first of these began & when production ended. Production could have continued into 1919, so there is likely a manufacturing "window" of about two years or a little longer.
The gun was most likely shipped to a military depot & I don't know if any of these military 1917s are worth the cost of a factory letter to learn the actual shipping date. That is for you to decide.
It is my understanding that after WW1 some of these revolvers were transferred to the Post Office Department, which later surplused them. Army guns were also surplused to NRA members through the old Director of Civilian Marksmanship or "DCM" (predecessor of the present Civilian Marksmanship Program--CMP for short).