Howdy
First of all, S&W does not always ship their guns in serial number order. Some sit in the warehouse longer than others. If you letter the gun, Roy Jinks, the S&W historian can only tell you when it shipped, not when it was made.
I can tell you that I bought my Model 19-3, SN 7K475XX brand new in the box in 1975.
According to the Standard Catalog of Smith and Wesson, K serial prefixes for the models 14, 15, 16, 17, 18, 19, 48, 53, 66, 67, and 68 for 1976 ran from 9K10001 through 9K999999.
So 1976 is probably a pretty good guess.