Nope. Japan invaded China in 1937. The invasion of Poland was in 1939.
And Genghis Khan attacked Western Xia in 1209 !
But that wasn't the start of the conflict we call WW2.
Invasion of Poland is not the start of WW2 either. September 1939 Poland invasion merely started Britain's and France's engagements with Germany turning a border war into a regional war. Russia and the USA were at peace at the time while other regional wars were going on.
- Operation Barbarossa was June 1941 which brought Russia into the war against Germany
- Pearl Harbor in December 7, 1941 brought USA into the Asia regional war
- Germany declared war on USA on December 11, 1941 - this joined the Asia/Europe wars into one
If you consider the start of any of the belligerence nations starting a fight with each other as the start of WWII, Japan's invasion of China (Marco Polo Bridge incidence) would probably be it. But that was a regional war. Not until Asia and European regional wars were joined that the regional wars were thought of as different theaters of a single war - a World-War.
According to Victor David Hanson (VDH): even at the time, it was not thought of as world war until late 1941. VDH is not your run-of-the-mill farmer. VDH is a Senior Fellow in classics and military history at Stanford University's Hoover Institution and chairs the working group on Military History. So I consider him an authority on the subject.
You can listen to him saying that (WWII wasn't thought of a world war till late 1941) on his lecture at Hillsdale on
Why WWII Matters here: