You are confusing belief with theory. Theory is the basis of science. Belief is the realm of religion.
And if you are a two dimensional creature living in flatland, there is no way for you to directly prove that there exists a third dimension. Well unless some external force rotates you along an axis out of your two dimensional space.
But higher dimensions would be a very clean and intuitive solution to some of the paradoxes in Physics. Take for example the creation of a proton-anitproton pair, and deflecting them in opposite directions then once they are sufficiently far apart deflect one and watch the other react in >c time (ie reacts before the light from the other particle of the pair can reach said particle). How can one of the pair react to an action done on the other in less time than it takes light to travel the distance? If the pair are linked in a higher dimension space, it's possible for one to react by "seeing" in less than c time if the higher dimension has a shorter light path.
I'm not saying that is any sort of theory proposed by anyone, or that it is some sort of proof of higher dimensions. It is however a valid sort of topic for investigative experiment to seek out verifying the existence of higher dimensions. Since math and physics agree that higher dimensions are possible, it's much more logical to assume they do exist and try to prove that than to presume they don't exist and try to prove that.
All theory requires making an assumption. It's far easier to assume the positive and try tro prove that. Provided you have some reasonable approach to making attempts to prove.
Only if you admit there is no way to prove a hypothesis, should one say i don't believe in the existence of X. One can't prove the Existence or Nonexistence of God. There is no experiment we can imagine to do so. Therefore there is no reason to believe in God nor any reason not to believe in God. It's irrelevant, and has no place in science. It's like believing there are only three dimensions, because we can't "see" or "prove" a fourth. That in itself is an act of faith.
Science is all about trying to explain things, not saying well "we don't know". If math indicates the answer is due to higher dimensions, Okham's Razor would indicate the rational conclusion is there ARE higher dimensions. The simplest solution is usually the answer. Plus math is pretty good at predicting actual reality and the real world. Math indicates that if you add one apple to a pile of thirteen apples you will have fourteen physical apples. Threfore the realistic perspective is to conclude if math predicts greater than 3 dimensions, it's realistic to assume math is correct and there are actually more than three real dimensions.
Simply saying, "I/we don't know" is equivalent to saying, I/we refuse to speculate on the cause. It might as well be happening by magic. I'm not saying anything in the real world indicates there are higher dimensions, but to me, it is simply one more hypothesis that needs experimental proof and a valid research/theoretical topic.