Howdy
It is a bit difficult to come up with an exact year for your 38 Military and Police Model of 1905, 4th Change, because the Standard Catalog of Smith and Wesson lists a huge block of serial numbers for that model. Starting with 241,704 in 1915 through 1,000,000 in 1942.
The 38 M&P at the top of this photo is SN 6699XX and it shipped in 1938.
This round butt 38 M&P, SN 6731XX, shipped in 1939.
As you can see, S&W did not always ship revolvers in the order they were made.
Still, I would hazard a guess that your 38 M&P, SN 862xxx, shipped some time in the 1940s.
I just posted your question on the Smith and Wesson Forum.
Let's see if I get an answer.