Clearly, the hostilities that became WWII started before 12/7/41.
When the war was appropriately categorized as a World War is a different date. Perhaps it became a world war when Japan and the US became part of the picture. At that point, hostilities were no longer confined to Europe but expanded to include North America and Asia as well.
It was a global concern by September 10, 1939. Canada, New Zealand, Australia and South Africa were all involved by that point.
You're only given a little spark of madness. You mustn't lose it. Robin Williams Alix