laytonj1 has already provided the model/serial number range. It's a reasonable estimate it was made right around 1920. It is unlikely it was made earlier, as during WWI S&W was busy making large frame revolvers in .45 and .455 for military use. In fact production of all revolvers except these large frame models was suspended for nearly a year in order to meet military demand.
The full name was S&W Hand Ejector Military & Police, more conveniently called the M&P. It was introduced in 1899 on the intermediate size K frame and became S&W's most famous and most prolific revolver, with production in the millions.
Skeeter Skelton in an article on the M&P noted how glamor guns like the Luger, P-38, Broomhandle Mauser, Colt SAA and so forth get all the attention in books and movies. But the plain, simple, unpretentious M&P probably took care of business more than all of them combined.
When S&W adopted a model numbering system in 1957 they began at number 10, assigning it to their dependable workhorse of a revolver, the M&P.
S&W began making M&Ps in .38 S&W for British service on March 11, 1940, continuing the regular serial number sequence and producing over 6,100 revolvers a month. By April 24, 1942 they had reached s/n 1,000,000 and had to begin a new numbering sequence. They chose to use the letter V as a prefix. The "V for Victory" slogan had already been made famous by Churchill. This was only about four months after Pearl Harbor and of course everyone was hoping for a quick victory.
Most had just the V prefix. A new hammer block safety system was added at the end of 1944, from then on the prefix was VS (a very few were stamped SV. On these the V and s/n had already been stamped so they just added an S in front). The last Victory model was s/n VS811119 made August 27, 1945. When commercial production resumed the V was dropped and the S prefix retained.
I went into some detail as there is a common assumption any M&P made in WWII is a Victory model. In fact a considerable number, likely in excess of 100,000, were made for military use before the V prefix was adopted. Collectors only use the Victory model term for those with a V in the prefix.
This information is from the fine book "A History of Smith & Wesson" by Roy G. Jinks, published in 1977 and since reprinted at least 13 times. I'm very lucky to have a personally autographed copy and find it an excellent reference.
This old revolver is a good example of one of the all-time great handguns.