How can G-d be proven?
The most common argument for the existence of G-d and the divinity of the Torah among all Jews- Talmudist and Karaites alike, is the Mass Revelation argument. It goes like this; there were 3 million whiteness of G-d speaking to Moses at Sinai, and this cannot have been faked.

The common counter argument is that there is no reference to this event outside of the Torah, now this is kind of irrelevant; the Mass revelation argument rests on deductive, not inductive reasoning,thus the Torah doesn't have to be assumed true beforehand enable for it to apply. This is because the argument deals with the introduction of the Torah not the Torah itself.
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Let me explain.

The three possibilities
It is an automatically assumed fact that Jews believe in the Mass revelation, this is because their parents told them about it,and their parents before them told them about it and so on. So, there must have once been a group of Jews from which this belief came from, this being the first to pass it down and teach it to their children.

Now the way I see it the Torah was introduced to these people in one of 3 ways, those are; they were lied to, they were lying, or they were telling the truth. So through the process of elimination we will dismiss all of the impossible or nonsensical possibilities with deductive reasoning.

Possibility #1; they were lied to:
This is nonsensical to assume, you could rationally conclude that Muhammad lied about his revelations, but not that Moses did, and here's why- mass revelation. Muhammad could claim that he received revelations from G-d alone and a lot of people would take his word for it, but it is impossible for Moses to have lied about his revelations without everyone knowing since part of these revelations is that everyone was there to see it, and if they weren't, then no one would accept it.

Here is how Rabbi Mizrachi explained it:
"If I went to 3 million people, and I told them that they all were slaves in Japan, and that I led them across the Ocean into Canada, and that I made it rain food, and we fought Giants, and that G-d spoke to me in front of all 3 million of them, and he gave me this book, they would say 'Rabbi, maybe you're not feeling well- we never lived in Japan, you never made it rain food, we never fought Giants, and we never saw G-d talk to you!' That would be it for my book no one would accept it."

So obviously it wasn't introduced this way, with Moses walking along and telling everyone that the Exodus happened- it would never had worked.

Possibility #2; They were lying:
Another common counterargument is that the Exodus didn't happen and that "they just told us that it did," but this is in essence just a conspiracy theory; that all the Jews got together and colluded to say that G-d spoke to all 3 million of them- and for what?

So that they would have to get circumcised? It makes no rational sense why they would do this, and it is impossible for such a large scale collusion to have taken place. Thus we are left with the third and only possibility.

Possibility #3; they were telling the truth:
"Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth."
Fact is there are no other possibilities as to how the Torah was introduced other than that it is true. So if you can find another possible way that the Torah could have bee introduced, then my entire argument fails, but until then it still stands and by deductive reasoning we must conclude that the Mass Revelation at Sinai really happened.