It looks to me like it could have been a Leader Novelty product. In addition to the baseball set from circa 1929, the company issued military cards in the early 1940s and Superman cards around that time. Here is an envelope from a 1937 contest they ran:
Curiously, the company was issued a cease and desist order from the FTC that was later upheld in court, which precluded it from operating what the government considered a lottery. I do not know the underlying facts as to what was shut down, but the decision was entered in 1937, so it very well could relate to the contest promoted by the envelope. BTW, a skosh of research also made mention of a similar order pertaining to Rittenhouse Candy--see E285 and the "game" played there.
Anyway, look at this box-front card catalogued as R3 Adventures of the Army and Navy / Adventures of the Army, Navy and the Marines, from the early 40's (examination of ebay examples shows perforations on at least two sides)
To be fair and accurate, only the Navy cards used the same color scheme as the OP's item; still, the box contained a coupon that could be removed from the perforations, and it also contained a card--both of which identified Leader Novelty Co, apparently on the inside only.
Finally here is the Superman issue from 1940:
It seems to me there are some similarities to the OP's All-American Candy & Toy box-- no ID of the company on the outside of the box, similar size, a reference to coupons and roughly the same color schemes and drawings. Food for thought anyway.