
In the early 1930s, "The Sportsman" had a three-bird roll-stamping on the sides of the receiver and the name "The Sportsman" was roll-stamped on the side of the receiver.

In the 1937-8 time frame, Remington Arms Co., Inc. revised the roll-stamping to one bird on each side of the receiver and started putting it on the
Model 11 receivers as well, and they began roll-stamping Model 11 or "The Sportsman" on the breechbolt at about this time.

They also dropped the separate serial number sequences for "The Sportsman" and began numbering them right along with the Model 11s.
Bottom line, I'd estimate your 20-gauge "The Sportsman" was made in the 1933-34 time frame. When combined Model 11 and "The Sportsman" 12-gauge serial numbers reached 499,999 on August 1, 1943, they jumped to 700,000 and continued.