As much of an Urban Legend as it sounds, the abbreviation G.I. was found as a "semiofficial army abbreviation of “galvanized iron,” used especially in inventories to describe iron cans, buckets, etc.; by 1917 it was also interpreted as an abbreviaton of “government issue,”… This from Random House Historical Dictionary of American Slang.
The term G.I. to mean a soldier appers in print in 1939.
The term G.I. Joe to mean an enlisted man appears in print in 1935. The in 1942 as a cartoon by David Breger.
As a point of interest, G.I.Jane first appered in print in 1944, NYTimes, to mean a member of the WAC.