The Status of Mount Sinai and Appeal to Halacha Authority

I have a fundamental question about Judaism and the status of Mount Sinai that has been burning in my mind for some time, and I have not been able to find a satisfactory answer to it.
As I understand it, the presence of Mount Sinai and the giving of the Torah by the Creator is the foundation of Judaism, without which Judaism cannot exist.
When I was young in yeshiva, I had questions about the status of Mount Sinai, whether it existed or not. In my search, I found several answers that satisfied me, my mind was at ease, and I was able to move forward relatively calmly with the other questions I had in Judaism.
Among the answers I found were:
1. The Prolonged Mass Revelation Argument
2. It was promised that the mass apparition would not happen again.
3. The Witness Argument/Tradition from Father to Son
4. The argument of honor, who took on illogical commandments
5. The transplantation argument, that the Torah stories could not be transplanted into later generations
6. Continuous memorization of the Torah commandments (Mitzvot Ta'T) throughout the generations

Recently, I became interested in the scientific method and discovered a method for reaching as accurate conclusions as possible by understanding logical fallacies and cognitive biases, and suddenly I was able to identify all the fallacies in the above claims (circular argument, ad populum, argument from lack of imagination, hasty generalization, false dichotomy, straw man, etc.).
(We can expand on the failures later)
Especially in light of Carl Sagan's standard, who rightly argued that extraordinary claims require extraordinary evidence.
That is, if I claim to have a 40-inch screen at home, then there will probably be no reason not to believe me. But if I claim to have a 2000-inch screen at home, you will of course want to see some shred of evidence that televisions of that size are even manufactured.
And since at Mount Sinai they want to prove not only a human gathering and the reception of the Torah, but also a metaphysical appearance of G-d and that He spoke to the people of Israel, and in addition also commands us to do or stay away from things, then the evidence needs to be much, much stronger than a natural case.
The only answer I was able to find to my claim is that if the status of Mount Sinai had been passed down with complete knowledge from generation to generation, then we would have had no choice, because then the very reality of God and the truth of the Torah would have been as clear to us as the sun and we would not have been able to act against it or commit transgressions. And that is not what God wanted.

This answer does not hold water because even in the Bible itself, the people of Israel, both after what they saw in the parting of the Red Sea and immediately after the giving of the Torah and the divine revelation, committed several sins.

But ultimately my biggest question on this subject is about God.
How is it possible that he can come to us with accusations about whether we are sinners or judge our behavior for heaven or hell and the next world if the evidence for the status of Mount Sinai is such weak evidence???
Did he want us to rely on faith without good evidence or just feelings regarding perhaps the most important decision in our lives and the purpose of the world??
And if you ask me: So what evidence would you like to receive to believe that there was a Mount Sinai event? I will answer you that God knows better than all of us what can satisfy us and allow us to believe in the authenticity of the Mount Sinai event.
 
 

And in addition to the status of Mount Sinai… this question also applies to the very method of determining halakha in Judaism, which suffers from a very serious problem called appeal to authority.
For example: Rabbi A claims that going to the army will kill and not pass, and Rabbi B claims that it is a mitzvah from the Torah that must be performed. Each of them can bring countless evidence and arguments to support the correctness of their opinion, but there is only one truth, and neither of them can truly prove that he is the one who is right and not the other Rabbi.
Therefore, all that we listen to a particular rabbi and not another is because of an appeal to authority, meaning that we believe him and trust him that he understands and that he is truly the one who is right.
And as you probably know, appealing to authority is a logical fallacy that can sometimes lead you to the truth and other times not.
The example I gave is only a contemporary example, but my question is also about the Tan'am/Amoraim and perhaps even about those that preceded them…
And here comes my question again..
How is it possible that he can come to us with claims about whether we are sinners or judge our behavior for heaven or hell and the next world if even the evidence of the teachers of the path on his behalf to justify their opinion is such weak evidence???
Did he want us to rely on faith without good evidence or just feelings regarding perhaps the most important decision in our lives and the purpose of the world??
 
 
I'm sorry for the length. But I'm very interested in your opinion on the subject, I really hope you might be able to shed some light on things I didn't notice 🙂