One thing most atheoskeptics seem to believe is that the burden on proof when it comes to claims of God's existence and the truth of Torah is on the believing Jew, not them. They seem to base this on the idea that since it takes no effort to claim nothing's out there since, according to the simple report of our physical senses that would seem to be the case, the concept of the existence of a supernatural being is therefore what needs to be proved.
It would seem to me that the opposite is true. Recall that Chazal tell us the opposite from this position in the gemara when they note in many places that being stingent is easy, but being lenient requires a stronger position. Yeet we know that many times the lenient position is the correct one and by taking the easy way out and acting stringently one misses out on the optimal performance of the mitzvah in question.
With this in mind, let us reexamine the question: on whom is the burden of proof? I would suggest that it's on the skeptoatheists. Consider, for example the question of the integrity of the Torah. The opinion that the Torah is a unified whole completed at the time of Moshe Rabeinu's death (excluding the last 8-12 verses according to those who hold that Yehoshua wrote them) and that the Torah text we have today is 99% accurate to the original is certainly older than that of the Biblical Critics who only started their research around 200 years ago. (Yes I am aware there are older critics than those who descended from Wellhausen but the modern school of Biblical criticism starts with that renowned anti-Semite) Consider further that all the so-called proofs brought by Wellhausen and his ilk were already known and commented on in the preceding 17 centuries by Chazal down through the Acharonim. Ideas such as God having multiple names with different ones being used in the different narratives, discrepancies between two versions of the same story, seemingly repetitive narratives or laws, irregular language usages and foreign words, all these were encountered by and explained by various commentaries throughout the millenia. On whom in the burden of proof? On Chazal and their successors who have a rich and consistent tradition, or on the Biblical Critics whose theories rely on several "scrolls" with one-letter names whose existence has never been proven? Tradition vs invented solutions to already explained problems? Only a determined atheoskeptic whose mind is made up before even examining the facts could endorse the latter upon serious consideration.
Then there is the existence of God. On a basic philosophic basis, the question can be answered both in the affirmative and negative quite satisfactorily. Anyone who tells you that God can be philosophically proven to either exist (of course!) or not (chas v'shalom) is misleading you or ignorant of his own limitations. Similarly in the physical domain, with apologies with Stephen Hawking, there is no conclusive proof either way of God's existence or control over this universe. Belief in God comes down to just that: belief, faith, an emotional feeling in the absence of definitive proof. Why is it the Navi says that a tzaddik lives by his faith? Because the only real life in the life in theWorld to Come and only faith will get your neshama there intact.
But that brings us to the burden of proof issue again. The universe clearly exists around us and both science and modern philosophy agree that it had a beginning. From the physical aspect, the important question is: where did the Big Bang come from? Stephen Hawking and his group would have us believe that one possibility is that matter appeared out of nowhere despite the possibility existing only in theoretical physics and without any actual precedent in the real universe. Others suggest that the Big Bang was the remnant of a previous universe that contracted at the end of its existence, only to re-expand to form ours. Again, a great premise for a sci-fi story but without any actual real proof. Where did the Big Bang come from? We have an established tradition that the First Cause, God, created the Big Bang and can hold by this since the definition of God is that He has no beginning and therefore could precede all of reality as we know it. The physicists, on the other hand, have theories without substance. On whom is the burden of proof?
Mind you, all of these arguments rest on the assumption that there must be a conflict between Torah and science, a position held by extremes on both sides of the debate. The more moderate middle ground, however, understands that since God created the universe there can be no real conflict between the two since science is merely the physical expression of God's creation. We must not give in to the arguments of those who insist that there must be a problem and then suggest simplistic and incorrect answers for it.