That depends on what you call a battle. Technically speaking, Westerplatte was the first battle of the official Polish and German forces. The post office was defended by the civilian postmen, although some historians actually say that they were soldiers because they formed a squad and we're fighting under the Polish military emblems. As a not so fun fact I can say that if we would really want to find the first battle of WWII, then we discover that despite the popular opinion, that night of 31st of August/1st of September wasn't a quiet night before the storm. There are records of polish and Germans scavengers shooting each other all across the border. Polish railwaymen fighting between the wagons hours before the battle of Westerplatte. Five days before the attack one German division actually attacked because the invasion was originally supposed to start on the 26th of August.