Are you asking in reference to one of the single action Model 3's or one of the double action New Model 3 S&W revolvers?
Most are antique and only a very small number of the total production would fall outside of the antique date range.
The Model 3 was comprised of 5 separate versions, the first 4 being single action and the last the double action New Model 3 -
1. The American Model - made from 1870 to 1874
2. The Russian Model - made from 1870 to 1878
3. Schofields - made from 1875 to 1877
4. New Model 3 single action - made from 1878 to 1912
5. The New Model 3 double action - made from 1881 to 1913
The New Model 3 revolvers were catalogued from 1878 to 1908 by S&W in .44 Russian.
In the Standard Catalog of S&W revolvers book for the New Model 3 chambered in .44 Russian it only gives an estimated range of years. For serial number range 14000-20000 it lists 1883-1890. For the .32-44 Target it lists serial number range 1-4333 from 1887-1910. Total New Model 3 serial number range was 1 to 35796 with serial # 35796 being shipped in 1912. Sorry I can't be anymore specific.
But I can tell you that serial number - 30392 was shipped from the factory in 1896 and serial number - 33197 was shipped from the factory on Sept. 1, 1898.
As for the New Model 3 double action revolvers, their serial number range was - 1 to 54668, with all double action revolver frames being made before 1899.
A highly decorated and engraved DA revolver serial number - 23060 was made in 1891 and shown at the 1893 world expo. And walnut grips with "S&W" inlays will be found after 1900 at serial number 53590.
Also according to the authors of the book all the frames were made pre 1898 and 1899 and then built up into complete revolvers as needed or as ordered up into the early 1900's.
additional info, serial # 22593 was shipped from the factory to St. Louis Mo on sept 10 1891