Seeking grandfather's WWII service records

Hi, through I have a copy of my grandfather's WWII registration card. In red type at the top, it lists "12-15-45 Ind. Army" and "12-24-46 Hon. Disc". His enlistment record shows he was enlisted at Turlock, CA and his rank was private, no branch assignment, regular army component. My question is whether there is a way to find out where he was during that year? The war was over. I thought maybe he was at Turlock decommissioning the place, but would love to know where he actually was. I do have his SSN, but when I looked into military records, it appears that I'm not a direct relative so can't request records. Maybe I'm wrong? Thank you for any guidance you might have.