scooterfiend
As others have noted, the .32 Winchester cartridge is better known as the .32-20. Your revolver is a K frame, whereas most of the S&W revolvers chambered for the .32 Long are I frame guns and ran in a different serial sequence.
A .32-20 Hand Ejector like yours would likely have shipped from the factory in 1908 or early 1909, but since they did not ship in serial order, that is only an estimate. I show three units in the 42000 range that shipped in December, 1908. I also show one in the 41000 range that shipped in September, 1908. I show two in the 44000 range, just a few numbers apart, that shipped in June, 1910 and December, 1909 (the former has a lower number than the latter). So you see it is a bit of a guessing game as to when .32-20 revolvers shipped.
To make it more complicated, there was a run of K frames, numbered in the .32-20 sequence that were actually chambered for the .32 Long cartridge, and those were in the 43000 range. Those units shipped in September, 1910. Yours is in the same serial range, but is clearly chambered for the Winchester (32-20) cartridge. The best we can do (guessing) is that yours probably left Springfield in the 1908-1910 period.