Skepticism towards a particular tool of cognition is good if we have a more successful tool to find out the truth through. Memories can be questioned if we have photographic documentation that can find out what exactly happened, and the sense of sight can be questioned if its truth can be examined using physical touch. But when we do not have such a superior tool, the logical choice is to rely on the tools at our disposal, because that is the best way we can get to the truth, and without them, we would almost certainly be wrong.
In the case of the Exodus from Egypt and the status of Mount Sinai, we see not only that the Biblical ancestors made as great an effort as possible to pass on the tradition, but also that these events created a strong impression on all mankind.
If we take the example of the Holocaust again, the reason that we believe in its existence is not only the testimonies of our grandparents, but the immense shock it caused to the world, which affected all levels of human culture, and its imprint is evident in them even today. Similarly, the revelation of Mount Sinai also left a huge impression on humanity.
Is it not amazing that of all the great empires and kingdoms of the ancient world, the book that most influenced the human culture is the Bible, the same collection of scrolls of a small flock of shepherds in a remote corner of the Middle East?
Furthermore, the two largest religions attribute holiness to it, and the stories and laws in it have shaped all levels of human culture, from art to politics, from religion to philosophy, and more.
If both the tradition of our Biblical ancestors, and the immense influence of the Bible and Judaism, are not enough to overcome skepticism, then probably nothing will. In this case, the problem is skepticism, not tradition. In the philosophy of science, it is known that theory is considered scientific only if it cannot be refuted; otherwise, it is meaningless. Similarly, unreasonable skepticism is therefore useless. As long as the skeptic does not present reasonable conditions in which he will be willing to accept the truth of the tradition (which does not include time travel, etc.), then his skepticism is merely a psychological tendency that should not be taken seriously, and certainly, it cannot tip the scales against tradition.