Welcome to the forum. The only sure way to get a shipping date on a S&W is to spring for a factory letter. There is no internet source for S&W serial numbers, but you can find some good serial number/calendar year approximations in the back pages of The Standard Catalog of Smith & Wesson (Supica and Nahas).
The problem is that Smith never recorded manufacturing dates -- just the dates on which guns left the building. Obviously the gun had to have been manufactured before it could be shipped, but Smith had no policy that mandated shipping in serial number order. Thus one can find guns with higher serial numbers that actually shipped months ahead of guns with lower numbers.
I can tell you as a kind of statistical approximation that a lot of other M&Ps with S/Ns around 500000 were shipped in 1925, and that's the best guess for your gun as well. If it got caught in one of those first in/last out situations, it might not have left the factory until 1926.
Haven't I seen that windowsill somewhere before?