It's really not a mystery. During WWII it was not at all unusual for a man from one state to be part of a unit which had its genesis in a state where he had never set foot.
The 145th Infantry was an Ohio National Guard outfit inducted into federal service in Oct 1940 and assigned to the 37th ID. They moved to Camp Shelby at that time, transferred to Penn in Feb 42, Calif in May 42, and went overseas the same month. After joining the Army (or being drafted) and receiving his training, he was no doubt assigned to the regiment as a replacement.