it doesn't really matter what the letters stand for.

This is American English we're talking about here, so of course the answer is ridiculously convoluted and involves everyone getting it wrong for so long that wrong eventually became right

It was originally an initialism used in U.S. Army paperwork for items made of galvanized iron.[2] The earliest known instance in writing is from either 1906[3] or 1907.[2]

During World War I, U.S. soldiers took to referring to heavy German artillery shells as "G.I. cans".[2][3] During the same war, "G.I.", reinterpreted as "government issue"[2] or "general issue",[3] began being used to refer to any item associated with the U.S. Army,[3] e.g., "G.I. soap".[3] Other reinterpretations of "G.I." include "garrison issue" and "general infantry".[3]

The earliest known recorded instances of "G.I." being used to refer to an American enlisted man as a slang term are from 1935.[2] In the form of "G.I. Joe" it was made better known due to it being taken as the title of a comic strip by Dave Breger in Yank, the Army Weekly, beginning in 1942.[2] A 1944 radio drama, They Call Me Joe, reached a much broader audience. It featured a different individual each week, thereby emphasizing that "G.I. Joe" encompassed U.S. soldiers of all ethnicities.[4] They Call Me Joe reached civilians across the U.S. via the NBC Radio Network and U.S. soldiers via the Armed Forces Radio Network. Gen. Dwight Eisenhower would notably reference the term "G.I. Joe," who he described as the main hero of World War II, in his May 1945 V-E address.