The term "golden sombrero" derives from the hockey and soccer "hat trick" (which signifies three goals or feats). Because four is bigger than three, a four-strikeout game is equated to a bigger, flashier hat—a sombrero. The modifier "golden" is simply an exaggerated reference to the scale of the player's struggles. [1, 2, 3, 4, 5]
The expression has distinct roots in baseball culture: [1]
The "Sombrero": In the 1970s, hitting a "hat trick" (three strikeouts) became widely known as simply getting a "sombrero" in baseball.
The "Golden Sombrero": When a batter struck out a fourth time in the same game, the concept was escalated to a "golden sombrero". The term frequently began appearing in print and sports journalism in the late 1970s and early 1980s.