While France and Great Britain wouldn’t declare war on Germany until September 3, 1939, the German invasion of Poland on September 1st was the last straw for Britain and France. It didn’t help that neither country did a lot to avert this turn of events and both did a lot to guarantee a war was going to happen.
While this was the start of the European portion of World War II, the Asian portion had been going for many years already, starting with Japan’s attack of Manchuria in September 1931, followed by their invasion of China proper in July 1937.