I feel like we should consider the Second Sino-Japanese War as the beginning because it was on such a large scale. I could be talking out of my ass, but I wish to hear it from you guys.
You aren't the first to make that suggestion. Just a few suggestions as to why...
WWI was used to describe what was basically a European struggle that was "world-wide" to the extent that the belligerents had global trade, colonies, and allies. (In fact, it's not clear whether the initial senses of the term really meant "a war fought on every continent" or just "a war involving the entire European state-system".) Even before WWII formally broke out, this term was used to describe a potential resumption of hostilities. The threat that the unresolved and poorly-resolved issues of WWI would lead to a new war was very threatening during the period, and the actually diplomatic chains of events in which these issues sparked a war culminated it September 1939.
To the extent that the Sino-Japanese war was a war at all, they were not "general wars"; that is, it was a bilateral conflict, rather than a world-wide one. It only became multilateral after the US and UK became involved. Also, strangely enough, neither side declared war until 1941 (thus the term, "China Incident"). Also, the war had a period of stalemate between 1938 and 1941 where no one gained ground and the Nationalists and Communists fought each other.