Absalom
SWCA Member, Absent Comrade
I never read an answer to the original question about age. As it turns out I've exhausted myself looking for the same info. And for almost the same 32. Mine has a 480*** serial, parkerized finish and ,after looking at Me239s pictures, the same wood grips. No import marks though. The closest I've come is maybe pre WW II. 400,000 was close to the start of the war I've read?....
I know nothing about the post-war Browning-branded US variant, so no help there.
But your 480xxx-range gun falls into an interesting period. There are no authoritative lists of serials with dates. But from Vanderlinden, some extrapolation is possible.
The Germans produced very few standard sized FN 1910s during the occupation, likely no more than several thousand; the focus was on the enlarged FN 1922 variant, of which around 450,000 were made from 1940 to 1944.
Vanderlinden documents a few 1910 guns that bracket your serial and thus provide at least a ballpark: a 1940 gun made at the beginning of the occupation, in the 470xxx-range, and a post-war pistol made for police in occupied Germany around 1948 in the 490xxx-range.
If your pistol shows no wartime stamps like WaA Waffenamt marks, it's likely post-war production from the later 1940s. I don't think the parkerizing is original in that case.