An important assumption of the Kuzari argument is there is a chain of national transmission of national events going back to the original witnesses of the Sinai-Exodus story. Moreover, national traditions of national events can not be introduced to a people. For example, people would say they have not heard such from their fathers. Thus national traditions of national events must be true or probably true. (Kuzari proponents may qualify which national traditions qualify for the Kuzari argument. For example, they may require a certain minimum number of people, or only certain kinds of national traditions etc: )
Can national traditions of national events be introduced without there being a history of such traditions amongst the bulk of the people ?
Lets see what the Tenach writes.
Judges2:8 And Joshua the son of Nun, the servant of the LORD, died, being a hundred and ten years old. 9 And they buried him in the border of his inheritance in Timnath-heres, in the hill-country of Ephraim, on the north of the mountain of Gaash. 10 And also all that generation were gathered unto their fathers; and there arose another generation after them, that knew not the LORD, nor yet the work which He had wrought for Israel.11 And the children of Israel did that which was evil in the sight of the LORD, and served the Baalim. 12 And they forsook the LORD, the God of their fathers, who brought them out of the land of Egypt, and followed other gods, of the gods of the peoples that were round about them, and worshipped them; and they provoked the LORD. 13 And they forsook the LORD, and served Baal and the Ashtaroth. 14 And the anger of the LORD was kindled against Israel, and He delivered them into the hands of spoilers that spoiled them, and He gave them over into the hands of their enemies round about, so that they could not any longer stand before their enemies.
Essentially Judges 2 informs that the bulk of Israel abandoned Yahweh worship, and fairly soon after the alleged Sinai - Exodus stories !. So who would pass down the alleged national traditions ? Would the Baalim worshiping parents inform their children of the revelation at Mount Sinai of the commandment "Thou shalt have no other gods before Me" Exodus 20:2 ? Or that Yahweh was the god who wrought miracles for their people in the Exodus ? Probably not. If so, at some later time the notions that Yahweh uttered at Mount Sinai “Thou shalt have no other gods before Me” and that Yahweh performed Exodus miracles were introduced by a smaller cadre of individuals or became believed for reasons other than national tradition In short, the alleged unbroken chain of national transmission of the Sinai-Exodus story was likely broken and a national tradition of a national events were introduced after the alleged events occurred.
Also consider these other examples which indicate national traditions of national events can be introduced into a mass of people even though they have no recollection of the traditions.
1) Ramban Numbers 15:22 9 - In the days of the wicked Kings such as Jeroboam MOST PEOPLE forgot the TORAH and COMMANDMENTS COMPLETELY.
[Thus at some future date the commandments must have been reintroduced to the bulk of the people. They were told the commandments were from G-d even though they had no recollection that these commandments being from G-d. Thus the national tradition consisting of G-d giving these commandments were introduced to a population having no record of such commandments. ]
2) Talmud Sukkah 20a - For in ancient times when the Torah was forgotten from Israel, Ezra came up from Babylon and established it.
[The bulk of the people forgot the Torah. Do they tell Ezra we have no recollection of this Torah from our forefathers and so we can not accept it ? No. So a national tradition consisting of this Torah was given to our forefathers can be introduced. ]