Kuzari must die
The torah claims that millions stood by Mount Sinai and saw the giving of Torah. Had someone not seen it, surely they would have objected and said that they had never seen it. Clearly, if this story were made up, millions would have had to conspire to say that it was not real. Hence, we have no choice but to declare the event genuine based on millions of eyewitnesses and their inability to conspire. QED.
What could break such a proof?:
Well, let's just say that the story did not begin at Mount Sinai. Let's say that people passed around stories over a few centuries that became syncratized, conflated, exaggerated. Not that such a thing could possibly happen, but let's just suppose. Then, let's say there was some emotional attachment to one version of the story or another on the part of various tribes, but that there was a king who would like to lead all of them in unity and peace. What is he to do, with all of these people fighting over the very different stories that they heard relating to their distant ancestors, perhaps 10 generations or more back? (Note: I could not name a single 5th generation ancestor of mine, much less what they really stood for or lived for.) So, a Yiddishe kopf, he has an idea. Let's get all of the heads of the groups together and write a single story that satisfies them enough so that they are not willing to fight over the differences. Then, if we can get 80% to agree that life will be better under the kingdom than as separate warring tribes, we can drive out the 20% trouble makers and everybody is happy. So, Dave, as his friends know him, becomes royalty and strengthens his rule with unified customs and editions to the holy book until it actually prophesies his G-d's will for his eternal kingdom. Get rid of the 20% heretics and shoin, a Torah.
So what would we need to exclude the bubbah maisah that I concocted above.
1. The torah must have been contemporary with the events that it depicts. If it were written later, then "how did they lie?" would be replaced with "how did they know?" My zaide who told me the story is in the same position that I am, relying on what he heard before. He is no closer to the events than I am. What if the first guy in line was no closer than I was. So without clear evidence that the Torah was written and witnessed by contemporaries of its characters, my story is just as probable as its story.
2. The story must not have changed substantially. OK, let's say zaide saw it and agreed that it happened. What was "it" that he saw? If he did not see what the Torah says that he saw, then again, I have no proof, no need of a conspiracy to propagate the story.
3. Third party corroboration would really help. The Torah describes world changing events, the destruction of government of Egypt, the splitting of the sea, the escape of 2.5 million slaves from a total population of 3 million (including the slaves), a violent revolutionary invasion of Cana'an, powerful kings and kingdoms wrecked, and the establishment of a new order in the world, one that the Egyptians did not recover. We may not be able to corroborate all of these, but we should be able to match many of them to historical events, at very least the contemporary existence of the people and places involved.
4. Much is also made of the fact that the Torah records the infighting and failings of its heroes. This, they will claim, is unheard of in the types of contemporary mythology which become national stories. So I will add a fourth assumption. The "uncommonness of this assumes that all of the Torah was written at one time, by one person or by people of similar viewpoint. Suppose, as our story does, that warring factions took pieces of their own texts and joined them together. Some of the factions praised hero X, some pointed out his failings. When they finally agreed, both versions survived the cut.
So essentially, the Kuzari depends on the "ikarrim" of Jewish faith, but those premises are not proofs of anything (and do not claim to be), just points of faith on which the edifice rests.
Until these conditions are proven independent of the ikarim, the Kuzari proof falls flat for anyone outside the faithful who already believe it. Not that any frum person should fret the lack of proof for their religious beliefs, I just hope that they will not trumpet this type of apologetic nonsense in the name of Judaism in a room full of intelligent people.