You can't. The best you can do is find out when it left the factory. Call S&W and they will tell you.
Call S&W and they will tell you when it left the factory. It could have been made a week to a year before.
By the serial number.
Call S&W and they will tell you.
Call S&W and they will tell you.
Call S&W and they will tell you when it shipped from the factory.
If you call S&W, they will tell you when it left the factory.
Call Smith and Wesson and they will tell you when it left the factory.
1955,1947
S&W will tell you if you call them.
Someone over at smith-wessonforum.com might be able to tell you.
1968
Impossible to answer without the sn. call SW with the sn and they can tell you.