Science does not have, at this time (although with a question like that, it probably never will), the ability to answer the question you posed. There have been hypothesises about it. One that always made sense to me, but looks less likely given new evidence, is that the universe, thanks to gravitational forces, eventually collapses back in on itself creating another "small icredibly dense amount of matter that was the nucleus of the ENDLESS expanse of BILLIONS of galaxies we see and was the source of what we see around us today" which then created another big bang, etc. Like the circle of life, but with the universe. In that instance, one could assume that the universe has just always been there. I know that's a big idea for any person to wrap their head around, that something didn't just come from anywhere, that it just always has been, but honestly, to me, it's not really different than believing that God has just always been (yes, I realize that you said not to do that, but if you're going to toss out impossible questions like this, you can't restrict yourself from taking them back).
Anyway, I kind of rambled, the point was, as of right now, while there are several hypothesises about the creation of the universe, since the event itself is not observable, testable or ortherwise capable of being quantified or measured, there can be no working theory about it (side note: there's a general misunderstanding here, from both sides, about the difference between an hypothesis and a theory. They are not the same). Someday, we may be able to figure that out, but I doubt it. Ultimately, the question of where everything came from, I believe, will be a question for religion and philosophy.
So, this was all kind of a long way of saying that the answer a real scientist would give you is, "I don't know". Now that answer, contrary to what you believe, does not destroy the whole foundation of science. It's just a question that science can't answer right now. At some point, every part of scientific knowledge that exists today was something that science couldn't explain. Somebody had to come along and make the observations and do the experiments. Science never claimed to have the answer to every question (although it often does come off as arrogant and "know-it-all"), and many scientists believe that we will never be able to answer every question. But that doesn't mean science is wrong.