Feel a little confident that there might well have been Kurds on the Beaches of Normandy. They have a wide Diaspora. The first identifiable Kurds to arrive in the USA did so following the First World War. Back then Woodrow Wilson was all about self determination, and in the Middle East the US policy was that the Kurds who were finally free of the Ottomans should be allowed their homeland. The British and the French had other ideas. In the early 1920's Iraq revolted against British occupation and the Kurds saw their chance at a homeland, they too took up arms against the British. There were two Kurdish rebellions, both of which were put down rather brutally and in the aftermath some Kurds found their way to the United States.
Not good at math but you have to reckon with the enlistments in the USA that followed the USA's belated entrance into the Second World War, the Pearl Harbor incident in the December of 1941, some Kurds might have received their draft notice, along with German Americans, Japanese Americans, Austrian Americans, Andaman Islander Americans.. It's a long list. And I'm aware that during the Second World War the US had a fully fledged and well institutionalized segregation, the military was no exception. But if you're a whitey-white person and you met a Kurd in the streets of Nashville you'd think he or she was as whitey-white as you, only with a very much better complexion.