Try this 2-part answer on for size: We don't know for sure. But that doesn't mean that we _can't_ or _never_will_ know.
Those who use god(s) to explain the existence of humans and/or the universe are using the "god of the gaps" argument. This boils down to using god(s) to explain that which is currently unexplainable--the gaps in our knowledge.
The problem with the "god of the gaps" approach is that knowledge is cumulative, and every day our gaps in knowledge shrink ever more. Consider that a few centuries ago, people believed that disease was caused by demonic possession. Eventually, optical physics led to the invention of the microscope, which in turn led to the discovery of germs, which combined with biology led to the germ theory of disease, which is what we have today. Similarly, we now know that lightning is a weather phenomenon, and not Zeus hurling mighty spears to Earth.
Actually, inflation theory, our most accurate theory of cosmology, has some pretty rational explanations for how our universe came about. (FYI, inflationary theory supplanted the big bang theory the same way relativity supplanted Newtonian physics.) To that end you may want to check out a book called "The Inflationary Universe" by Alan Guth from your local public or university physics library.
By the way I don't mean to sound rude, but I do have a slight nitpick with your use of the phrase "whatever science dictates." Science is not a belief system like religion, but a methodology. Science & scientists are not meant to be taken on authority like religion is; the whole purpose of science is that its conclusions can be challenged if new data is discovered or a better-fitting theory comes along. Scientists do not take scientific conclusions on blind faith the way believers take religious doctrine on blind faith. The peer-review process makes sure any new theory is thoroughly vetted, and scientists can be quite competitive and critical. No scientific theory will stand simply because it's liked; it must deliver the goods.
Finally, from a purely philosophic view, why must there be a reason or purpose for our existence? We have free will, and thus a large degree of control over our lives. Is it not enough simply to exist? It seems to me that what's more important is not how we came to be but what we do with our lives once we're here. And introducing a creator god into the equation doesn't actually answer anything, because the next logical question is, where did this god or gods come from? If our universe requires a First Cause, why doesn't god?
I can't fully explain why anything exists. But what we do know, simply doesn't require the presence of a god. Gods are superfluous in that they aren't necessary, and add nothing to our understanding of the universe.