The traditions with boys and guns in the USA is directly (traceably) tied to marketing efforts from the 1930s and 1940s by gun manufacturers and gun associations such as the NRA (before it got all super weird).
They saw boys organizations such as the Boy Scouts as natural vehicles to sell their products and so they created a tradition where each Boy Scout would get a .22 Rifle as part of a sacred traditions, etc etc., much as the history of Greeting Carts as corporate constructed traditions and Santa Claus.
But prior to the 1930s, there was no such tradition in the USA as it was created out of whole cloth for profit and it worked; at this point, nobody much would be left alive to remember when it WASN’T father/son tradition. As far as they’re concerns, it’s just always been that way.