If you destroy every argument for Judaism, the believer, before admitting that he still believes in Judaism because he has faith, will likely play what I like to call the "epistemological non-sense game".
He will tell you that you cannot know everything. There is just so much we do not know. We have no idea where the universe came from. We see that the law of gravitation works but we have no idea if it will continue to work tomorrow. We cannot even know if other people exist or if they are just illusions in our head. Essentially they are imitating Descartes.
The point of this is to tell you, the skeptic, that all your rational pursuit of trying to understand the universe is meaningless because in the end none of us can really know what is true about the universe. They set up this situation because they want to show that your rational beliefs are at the same equal level as their irrational mythological beliefs. The Jewish believer (or any religion) will admit that he cannot know if Judaism is correct but neither can I know if my natural material deterministic universe is correct. This is what I call the epistemological non-sense game. This is all what this game is about. Furthermore, these religious believers may use fancy philosophical terms to make it seem as if all of that they say deserves any respect. They hide behind using fancy language and philosophical terms. But if one goes around those terms and words that they use what they say is exactly what I said in the paragraph above.
Yes I admit that I can never really know my own beliefs that I have now. However, this does not mean that your (referring to the religious Jew in second person) beliefs are on the same level as mine. Because I make an effort to come to my beliefs. I apply my reasoning skills and what we already can observe in the universe to try to come to the best possible belief that I can. As opposed to you. You make no effort to come to your beliefs. You might just as well pull your beliefs out of your anus and say that they are your beliefs. Skepticism does not mean that I know the truth. Skepticism means that I know what is not true through a rational processes. Skepticism is the rejection of false ideas through rational thinking. Religion is the acceptance of ideas without any rational thinking. So yes, I admit, I may be wrong in the end (I certainly do not think so as the chances for that happening are extremely low) but at least I was rational about it. As opposed to religion which is irrational in its beliefs. Therefore, your beliefs do not stand anywhere to the same level of respect as do mine.