Where was the first battle the US armor fought in North Africa where US tanks were defeated by Afrika Korps?

I think you are looking for Kasserine. Rommel was astounded by how well supplied the US forces were. General Fredenhall does not emerge with much credit. Had Rommel had the support of Kesselring or Von Arnim then the Afrika Korps victory might have been more far reaching, nonetheless the Germans were disinclined to see their tenure in North Africa was in its death throes. They sent reinforcements who enentually, most of them, became prisoners of war.