Yeah, that´s right, Zum!
Long ago (at the time of WWI and WWII), the Army and Air Force would standardize virtually all of their equipament, even combs, brush, helmets, uniforms were all standard issue (per government standards - so government issues). From equipment to the draft and then men doing military service was just a awhile away.
The soldiers themselves making the expression GI synonym with the military men themselves would be just a matter of time...
The general infantry of the forces came to be known as GI Joe, and were made into toys, and even collectibles sets (saleable) for children.
Just a bit of history.