Inspired by this:
For most of what's written in Tanakh, the only evidence that we have of its truth is Tanakh itself. Since many people are skeptical of a book with no independent sources backing up its claims, why didn't God wait to reveal himself until we had advanced enough to create audio and video recording devices? That way, there would be indisputable evidence of God's revelation.
the purpose of creation is to give man an opportunity to follow virtue of his own free will (See beginning of Derech Hashem). God does not like to do PUBLIC miracles unless it is absolutely necessary as it interferes with His plan. (source Tov Halevanon commentary to shaar bitachon ch.4 on the part where Shmuel asked G-d "How shall I go? For, if Saul hears, he will kill me.")
The Drashas Haran (forget the exact place) wrote that the giving of the torah had to be miraculous because there needed to be no doubt whatsoever that it was indeed from God. This is why it was preceded by the miracles of the ten plagues, and in Egypt which was the world center of witchcraft (so that people would not say Moshe was a sorcerer and if he did the plagues in Egypt, he would have been defeated). Likewise, Moshe was speech impaired so people would not say he was a great orator. And the final plague occured on passover, astrologically, the most powerful day of the egyption god, etc. many other factors.
That said, God was forced to make these miracles to prove the authenticity of the torah. The torah had to be given back then at the inception of the jewish people as this was His plan. If you ask, why did God withhold technology for so long, why didn't He allow it back then so everything could be recorded? I think the answer is that man is too dangerous to be given modern technology. Once you have recording devices, then you have electricity, transistors, and eventually nuclear weapons. Man is much too dangerous to be given these things in the middle of history. Therefore it was withheld until the end of days which we are in now.
Even had God waited until there were cameras and recording devices, there would always be skeptics who would deny it. However, if we define our terms we will find that there is no occasion for God to wait for cameras and recording devices.
If we define revelation to mean to reveal something then it is not true that revelation stopped at Sinai before there were cameras and recording devices.
Revelation did not cease; it is ongoing. It is not information that was revealed only through prophets. It is information about God contained in studying science and the world. The Psalmist explains:
“The heavens declare the glory of God and the firmament showeth his handiwork, — Day unto day uttereth speech, and night unto night sheweth knowledge.” (Psalm 19)
Following the path set by R' Yehuda Halevi, Rambam and more:
Our tradition is completely oral. Very few things were (initially) let to be written (תנ"ך), the rest kept alive by oral tradition.
As R' Yehuda Halevi writes in Kuzari - the Torah doesn't prove itself. The basis of Torah isn't the Torah. The very fact that is was passed down through the ages by many reliable people is strong evidence - as good as hard proof. That's why we believe it's true, and then we rely on all written. Otherwise you have sort of a paradox, as your question points out.
Besides - how would proof help? Even participating in a miracle doesn't mean you get everything straight from there on (see Ma'amad Har Sinai & golden calf) what would a video clip do better?
In Shmuel I chapter 7 it says: וינהו כל בית ישראל אחרי ה, the whole nation was yearning for G-d.
Real belief comes from hard work of education - והלך מדי שנה בשנה... ושפט את ישראל - he would go round every year and judge (generally "judging" also meant teaching Torah) the people (ibid).
Many people close their eyes to simple facts of reality. Even today there are people who have been through miracles (though not as explicit) and do not see the hand guiding these happenings.
Remember Pharaoh after 10 miraculous plagues leaving no doubt of G-d - chasing Israel into the sea. May none reach that level of blindness.
See Hosea 14:10
מִי חָכָם וְיָבֵן אֵלֶּה נָבוֹן וְיֵדָעֵם כִּי יְשָׁרִים דַּרְכֵי ה' וְצַדִּקִים יֵלְכוּ בָם וּפֹשְׁעִים יִכָּשְׁלוּ בָם:
Who is wise and will understand these, discerning and will know them; for the ways of the Lord are straight, and the righteous shall walk in them, and the rebellious shall stumble on them.
