Why not claim that the Jewish tradition is false?

Just as we assume that the Greek one is false.

And likewise with the Palestinian falsehood that has now been born before our eyes.
So if something relatively simple like the history of a people—we can see that in less than 60 years an entire people can change its past from a young people into one that feels ancient—

then all the more so regarding things that are mythological, like miracles and religious rituals.

This is too broad a question for discussion here. See the outlines for a discussion in my fifth notebook.

I read that notebook (and the rest of the notebooks too),

and I still think the Rabbi skipped over this part.

The Rabbi apparently wants to say that if the probability that what is described in the Torah could happen is reasonable, then we should let the tradition stand on its own claims.
Only if we think it is unreasonable—like Greek mythology (even though most of the gods are forces of nature)—should we reject its claims and say that it developed over time.

But still, if we see how easy it is to implant a tradition and national consciousness—see the case of the Palestinian people—
then why relate to a tradition at all, instead of simply rejecting its claims outright?
Even if there is a reasonable chance that the process it describes could really be true.
But the vehicle for transmitting the tradition—the people—is just so weak that it cannot really be relied on at all.

For example, we have no reason to reject the claim that the Palestinian people have been here since time immemorial. But it is still a lie that was completely absorbed in less than 60 years…

So how would we know that it is really false? Only if we have a broad front of sources on the matter. Otherwise we would not hesitate to reject it with both hands.

For example, if the only one transmitting the event to us is the Palestinian people—false.
Many peoples and history books—true.

Of course it could be that a people alone also transmits truth, but we have no ability to accept such a tradition.
Because, like it or not, national tradition is like an unverified promissory note, which is presumed forged.
A national tradition that is supported by broad historical writings from the same period (not a later period) is like a verified note.
(And the Rabbi shouldn’t say that Judaism has a broad front from Islam and Christianity, because Christianity previously believed in Greek mythology, so you can see how easy it was for it to believe falsehood; that does not count as a broad front for Judaism. And certainly nobody claims that it saw the revelation at Mount Sinai or was close to those events.)

The Rabbi didn’t really address this point very much. I would be glad if the Rabbi would address it more.

It is very easy to implant lots of things. It is very easy to deceive vision, and yet we do not doubt our vision. It is very easy to fabricate history, and yet we believe historical traditions (about Julius Caesar and Napoleon and the like). This is a matter of common sense, and examples of crooked uses of common sense add nothing here. An argument like this could attack any claim you can think of.
Beyond that, there is the whole set of considerations brought in the notebook, which combine into an entirely reasonable consideration. I do not see what more I can spell out beyond that.