Germany invaded Poland on September 1, 1939. France and Great Britain, via treaty obligations, declared war on Germany on September 3, 1939 ... World War Two starts ...
USSR invades Poland ... September 17, 1939 ... so Uncle Joe "joined" in AFTER the war had started two weeks earlier.
But the agreement to invade was made before the Nazis rolled, so the Soviets are jointly responsible.
As to when World War II "officially" started. Insofar as this article is about *Japan's* involvement, one should bear in mind that MOST of Japan's war effort (at least as far as troop strength is concerned) was directed against CHINA, which it had been fighting since it had precipitated the Second Sino-Japanese War in 1937.