I suspect 1946-47. You are hemmed in between very late in 1945 and 1948. The V as in SV was dropped as the leftover Victory frames were incorporated into the post war commercial inventory. The S prefix was the end of the second million M&P's. The C prefix debuted in 1948. Take a hard look at the butt it is possible it has a filled in swivel hole.
Welcome to the forums from the Wiregrass! Waidmann is correct. Your gun likely shipped in November or December 1946 since other guns with nearby serial numbers shipped in that time period. You might want to pull the grips and confirm the numerial part of the serial is stamped on the back of the right panel. If so, the grips are original to the gun...they look righteous to me. My S serial .38 M&P shipped a couple of years later than yours just before the C serial began in 1948.
I'd need to see more pictures of the gun with close ups of the bluing. From the one picture you posted, I see polishing marks on the frame and a scuff near the front of the trigger that appears to have been blued over. S&W would not have done that. It may have been refinished at some point before you got it. That knocks down collector value completely and it becomes a shooter. If the finish is original, it would bring between $500 and $600 in my area...maybe more in other regions of the country.