Yes, she's a beauty. Hardly shot at all, if any. Maybe just cycled. I'm estimating '56 or the next year since it's a 3 screw model introduced c. 1956.
But, if the serial # on the box is correct to the gun, the nearest #s I have in my database are:
7200 shipped in Nov '54,
75XX in 1954,
7531 in Dec '54.
But as you no doubt know as David said above, they didn't ship in numerical order. And the 3 guns above were all earlier 4 screw models.
REVISION NOTE: Based on the recently posted serial #, the closest # in my database to yours is # 29403, shipped Nov. 1957. So unfortunately, not likely to be a birth year gun but you never know for sure until you get a letter.