You can't really point to one single point and say "Yep, that's it!" but there are several places worth noting for how they impacted the expansion in scope and scale of the Second World War.

The first thing I'd point out is that it is possible to consider World War II not as one, single conflict, but rather several regional conflicts that happened contemporarily, and due to circumstances, came to be intricately connected. Japan and China, after all, had been at war for several years by the time Germany invaded Poland on Sept. 1, 1939, which is the 'traditional' start date for World War II; and the war in the Pacific was almost entirely disconnected from that in Europe and North Africa, since despite their nominal alliance, the principle Axis powers were never able to produce more than the most token of actual coordination.

The second piece is how even in the West, nearly two years of war going on between hostilities breaking out, and the German invasion of the Soviet Union which of course would be the largest front of the war in Europe, and then another half-year before America's arrival as a belligerent power (although we can of course compare that to America's late arrival the first time around too!). But then of course France fell in mid-1940, which was far more than Germany ever achieved their previous attempt so maybe that says something also depending on your metric.

The point I'm aiming to draw here is that even in hindsight, it is hard to say with clarity even in hindsight at what point the war transformed to "bigger" - itself an amorphous concept, given that you yourself include 'larger', 'more important', or 'more deadly', which are not all the same thing. Certainly by 1942, the war had expanded in scope far beyond that of World War I, which, although global, was waged almost exclusively by European powers, and was truly global in a way far beyond that of World War I, but you could say that even on Sept. 1, 1939 depending on your perspective, as some people argue fiercely that only including China as a part of the conflict after Dec. 7th, 1941 is simply illogical.

So far though I haven't really gotten to the heart of your question, and if anything, am being kind of wishy-washy, but it is because there isn't really a good, single, cohesive answer to it, least of all given that there isn't one even today. "People"... who are they? World opinion? Allied opinion? Axis? American? British? I would be hard pressed even on the national level to pinpoint a turning point, so I'm just going to evade the question on the macro level, and focus instead on the micro level, looking at American attitude to the conflict as exemplified by Sgt. Alvin York, who was arguably the most famous veteran of World War I, a national hero and medal of honor winner.

I've written about him before, which I'll be cribbing from and expanding on, but to preface briefly, I don't want him to be taken as representative of all Americans, just representative of one strain of American voice on the subject, but he is nevertheless notable for being an early proponent of Allied involvement in the war, and in my mind certainly fits what you are looking for in terms of offering the perspective of a man who saw the importance of the conflict, and given his own history, was speaking from experience.

Two decades after his heroics, as the Second World War broke out and America initially stood on the sidelines, the former conscientious objector turned military hero Alvin York proved to be a fairly vocal proponent for increased American involvement. Even prior to the beginning of “World War II”, York had shown himself to be a stirring voice against isolationism, and of the potential for American military power to be a guarantor of world peace. In 1937, as the Second Sino-Japanese War was already seeing hundreds of thousands of casualties in Asia, he rather insightfully noted the possibility that continued Japanese incursions would draw America into the war. Not only was he of the belief that the US needed to stand “ready to fight again in the interest of peace”, but even that the US ought to be more forceful and proactive - “I’d just as soon get into it now as later”. He also wasn’t sparing Hitler in his views, although initially less forceful about actual American intervention. Commenting to reporters at a memorial event held just in the wake of the Munich Agreement, he showed no illusions that Hitler would remain satisfied, opining that “If we want to stop Hitler, we must knock him off the block”. A few months later, as the world continued to inch closer to war, he told reports that the United States had a duty to rearm, and “ought too be prepared to defend the Western Hemisphere”, and although he expressed optimism that conflict might still be averted, he felt America needed a strong military in the event war did break out, for a bristling armed neutrality.

The outbreak of war in Europe, of course, only bolstered his views, giving truth to his prophecies, and shifting his mind from a mere necessity to defend America against potential invasion to the possible need to return 'over there'. In the fall of 1940, the United States having just begun the augmentation of its armed forces with its first ever peacetime draft, York was not only an active proponent of the measure, but offered himself up for active involvement as well. Although in his early ‘50s and well past service age, he served on his local county draft board. Recalling his own religions beliefs that had initially kept him from taking up arms, int was reported at that time that he was planning to speak with any local conscientious objectors in an effort to change their minds, similar to how his own had been in conversation with an officer.

As the war in Europe continued, he only became more vocal. In the Spring of ’41 at a banquet held at the Alvin C. York Institute, a private school he had founded, he beat the drum of war, strongly voicing that the United States had a moral duty to be involved, and castigating the isolationists:

America now stands at a crossroads. This is no time to compromise with Hitlerism. Those who advocate such a source are following the illusion which has already plunged Europe over the brink of annihilation.

Late in July, he gave a speech to the Tennessean Society on the necessity of continued aid to the beleaguered UK, noting that "we must give England every aid we can, and as quickly as we can". American 'boots' on the ground were still something that he had reservations about, but he certainly had no doubt about which side was right, and America's obligation to be backing them.

These speeches, in fairly small settings, were nevertheless notable enough for the national news, and later in the year, York words echoing similar sentiments would be heard on a much more national stage in any case. Even aside from his Gary Cooper staring biopic that came out win the summer of ’41 - a strong image of the American citizen-soldier for the audiences’ minds, and likely to “be useful in awakening America in a time of crisis” as FDR himself noted - on the Armistice Day (Veterans Day) ceremony at Arlington Cemetery, less than a month before the United States would find itself at war, Yorks earlier remarks from a Memorial Day speech were utilized by the President himself, who quoted his response to critics:

The thing they forget is that liberty and freedom and democracy are so very precious that you do not fight to win them once and stop. Liberty and freedom and democracy are prizes awarded only to those peoples who fight to win them, and then keep fighting eternally to hold them.

Whatever we knew or thought we knew a few years or months ago, we know now that the danger of brutality, the danger of tyranny and slavery to freedom loving people can be real and terrible.

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