GI initially appeared in the mid-30s and stood for 'Government Issue'. It was applied to virtually everything that a soldier might be supplied with, from soap to boots. Because the man and his kit became so closely associated, the letters came - but not until the 40s - to mean the guy himself.
I thought that it stood for GENERAL ISSUE which covered all the kit issued to all US soldiers [other than specialist kit issued to individual units etc]. Each item of kit is given a M [for military] number ,ie a M-1 is a helmet.