The question "How was the Universe created" has been researched by physicists for hundreds -- thousands -- of years, and most modern physicists agree that the Universe as we know it came from the big bang some eleven billion to fifteen billion years ago. They have the physics of what happened down to a few milliseconds after the big bang (perhaps I'm off by a few orders of magnitude. Regardless, they can "see" back pretty far). Of course, the big bang isn't really an answer to this question, since it doesn't tell us how the Universe was created -- only that it happened, and that the Big Bang is the best description we have for the early stages of the Universe As We Know It.
My goal is not to criticize this work with the Big Bang. That research has been carried out by extremely smart people, and it provides useful information for answering the present question. My goal is instead to explain why the original question is poorly formed, if it is even meaningful at all.
Why it doesn't make sense to ask, "How was the Universe created?"
This problem has its roots in that our intuition for the Universe is built up from our small glimpse of a very local part of it. We know about three three spatial dimensions and time, and we have results from some important scientific experiments. Einstein's relativity indicates that time is drastically different from how we perceive it. Only people who think hard about relativity have any intuition at how time works at the galactic (or super-duper-fast) level, and nobody--even physicists-- are really sure how it works at the sub-atomic level, which was really important during the Big Bang (many researchers have theories, but these theories are impossible to validate with our current technology). Some researchers even speculate that we may have more than one time dimension.
Our sense of time is defined by its relevance to us as organisms evolved to survive when living with the physics of the Universe as they exist at Earth-scale. There's no reason to think that this sense of time is particularly relevant at Universe-scale. Given its bizarre behavior and how little we know about it, it may be little more to the Universe than the sense of taste to a human -- great if you have it, but an afterthought if you don't.
Second, we have no indication that the Universe was created out of nothing. Our daily intuition clearly tells us that it's impossible to create something out of nothing, and without time before the Universe existed, it's virtually impossible for it to have not existed before it existed, because there was no before. You can't not exist at a certain time if time doesn't exist. These things, and our everyday experience with how things are created, suggest that the Universe was not created. It exists. (You may ask why I allow myself to use everyday experience as a premise when I argued against using everyday intuition about time. My point is that, if one is going to insist on using everyday intuition of time to ask these questions, then it's fair game for me to use our everyday intuition of causality to show why the question is invalid) We also have no reason to think that the Big Bang was an isolated incident, or that the Universe was created when the Big Bang happened. It's possible that the Universe was growing exponentially at the time of the big bang, halving in size every T units of time you look back. It's possible that the Universe periodically expands, contracts, expands again, and contracts again, ad infinitum. It's possible that time is a giant loop, and that it will repeat itself trillions of years hence. None of these are ruled out by the Big Bang. (N.B. I am not a physicist, but this is my "I-got-a-minor-in-physics" understanding.)
In short, it simply doesn't make sense to ask how the universe was created, when that question uses our conception of time, which is defined by the Universe itself. This is especially so when we have no reason to think that there is a beginning or end of time. Again, asking "How was the Universe created?" is like asking "What's at the edges of the Earth?".
This isn't to say it's not worth pursuing these grand questions, or that we shouldn't study the history of the known Universe. Rather, it's to say that we should be careful to ask our philosophical questions by framing them in terms that don't change with the object of the questions. Instead, perhaps it makes a bit more sense to ask the question, "Why does the Universe exist?" This question does not require time to be defined, when it still gets at the same issue.
So, why does the Universe exist?
This new question has its limits, again because we are basing this on our own sense of intuition and aesthetics. Still, I'll try my best.
First, this question is well-formed because of Descarte's original cogito, ergo sum: "I think, therefore I am". This statement is pretty much irrefutable, at least for the thinker. If I define the Universe to be whatever scaffolding it is that allows me to think, or to exist, or to think about existing, then it's also clear that the Universe does indeed exist. And it's perfectly legitimate to ask why it exists.
The next part of unraveling this question is establishing what we mean by why. When I ask why the Universe exists, I am asking why does it exist, instead of not existing.
The alternative: the Universe does not exist
When I think about the Universe not existing, I'll admit that my first conception is of a vacuum, a bit like in outer space, forever. Yet even this seemingly innocuous conception is flawed: there is no sense of time in a nonexistent Universe, and my conception of a vacuum assumes three spatial dimensions, ignoring the very fabric of the Universe that creates these dimensions. It is more accurate to simply imagine nothing, with no sense of time or space. A point, perhaps -- zero dimensions, with no sense of time or space -- may be the most reasonable approximation that we can conceive of. But remember that this point has no time -- it's a point, frozen in time, forever. Quite depressing.
Once the alternative to the Universe is framed in this sense, it's a bit less clear why the alternative -- pure nothing, or at most a point (i.e., zero dimensions) -- is in any way superior to the Universe as it is. Why should there be a point Universe instead of nothing? Tell me what nothing is, and how that differs from a point. I'll claim first that nothingness is equivalent to a point, and second that aesthetically a Universe with more dimensions is more preferable than one with zero dimensions. In fact, looking at it with intuition and aesthetics from information theory, the Universe should prefer more space to a point so that it has more room to spread things out in. This is because a single point has very little entropy, and the Universe would really feel much better if it weren't so cramped, by taking up four, nine, or ten (or more) dimensions.
But in my opinion it's actually harder to conceive of nothingness -- or a point -- than what we have. So maybe that's one (aesthetic) argument for why we should have the Universe over nothing. Because it's hard to conceive of the Universe otherwise.
Arguments from first principle
This still doesn't answer the question of why the Universe exists. But I would feel equally enlightened if I knew the answer to this question instead of my original question ("How was the Universe Created"), especially knowing that the original question is meaningless. I could also imagine some reasonable arguments from first principle in favor of the Universe existing, or in favor of the Universe trying to figure out whether it should exist or not, in a secular way, and (oh, snap) having to exist while figuring that out.
Another argument for the universe existing is that there are some logically irrefutable facts, such as "a triangle has three sides", or "two plus three is five". These are true, regardless of whether the Universe exists or not. If the Universe did not exist, wouldn't such facts still be true? Or is it necessary to have some sort of logical scaffolding, provided by a Universe, for them to be true? I find the latter to be unlikely. If it's the case that logic exists when nothing else exists, is it really the case that nothing exists?
I won't be able to answer this question here and now, as it's been pondered publicly by philosophers for hundreds of years, but I hope that this discussion was helpful nonetheless.