Steve, I found this info, it says 1956...don't know the source, I was just surfing around.
The base version of the Model 336, the Model 336A, was produced from 1948-62, and then again from 1973-80. Originally chambered only for .30-30 Winchester and .32 Winchester Special, a .35 Remington chambering was introduced in 1953. In the early 1950s, a decorative white spacer on the butt and white pistol grip wrist cap were added, but this practice was stopped in 1953, only to re-start in 1957. Starting in 1956, the Model 336A was drilled and tapped for a scope mount, and used Micro-Groove rifling. A hood was added to the front sight in 1957, and in 1960, the top of the receiver was given a sandblasted finish to minimize glare when sighting through the iron sights. When the Model 336A re-appeared in 1973, it had a straight wrist stock and a new Wide-Scan front sight.
Hope this helps, you might want to check some more sources and see if they say the same thing.
Jim