Firstly, and I'm not assuming that you intend a creator god to be the preferable explanation (though of course many do), the same question can be applied to that god. If one always existed, he/she just sat there for an eternity before acting. Why?
Secondly, models of an open, non-oscillating universe generally imply that time as we know it did not exist before (or as one apologist put it, "ontologically prior to") the Big Bang. As one part of Einstein's theoretical combination "spacetime", it was wrapped up with everything else in the singularity (speck) and its apparent forward flow began when the expansion did. Going by this type of model, it wasn't possible for anything to happen "before" the Big Bang. Stephen Hawking likened the question to asking what's north of the North Pole.
Thirdly, it's possible that there are systems of time and space outside the universe we know, and our universe was set off by one of these. There are various models of a multiverse, collectively infinite in both time and matter, where universes regularly beget other universes. There are also slightly simpler models of a single external mother universe or "metaverse" which spawns the others. These are speculative, of course, but at least the extra entities being posited are objects we know exist in at least one case, i.e. universes.
Finally, new evidence is emerging which may challenge the singularity's perceived lack of a beginning. It may be best to wait and see.
This is the Cosmological Argument. I've answered it most thoroughly here, but also to some extent here, here and in a comment here. Jake and Carl Sagan have their own answers here. Look through them and choose your own solutions from that lot to either accept or argue.
I'll just add that simply because the Big Bang seems to imply something which seems nonsensical to you doesn't necessarily mean that it is actually nonsensical, let alone impossible, or that it even implies what you think it does.
Nothing yet adequately addresses the reality of a rational universe, Jack, not even gods.
You're a little too focused on the multiple-universe hypothesis. It's not intended to be authoratively substituted for Creation myths in the same way as the theory of evolution can be substituted for religious accounts of the origin of modern animals. There's really no evidence for it yet, whereas evolution is supported by vast amounts.
The point of infinite multiple universes in these discussions is that there is at least one conceivable alternative to the hypothesis that an intelligent being created this particular universe to exact specifications, and therefore the theistic or deistic view cannot be presented as the only possible way. It's the standard response to the classic argument from ignorance, or as Dawkins puts it, the "argument from personal incredulity".
In simple terms, theists will often try to prove the existence of gods by pointing to something amazing and rhetorically asking, "How else could that possibly have happened?" The obvious response, in general form: "Like this, for example." Multiple universes are one such "this".
One other alternative hypothesis which serves the above purpose is that the universe is eternal in both directions, going back before the Big Bang. This removes the need for it to be created, or to emerge, or whatever, at all. Again, no evidence yet, but not impossible and therefore lethal to any attempted proof by elimination of a god's necessity.
But let's go in another direction. We'll take your stated view a bit further and reject as implausible (though not impossible) any unintelligent, undirected origins for our universe conceived so far, including the multiple-universe idea.
Where does that leave us? With an intelligent or directed origin, facilitated by an entity which can be satisfactorily described as a god. But then where did the god come from? If no undirected origin will suffice for a collection of matter and energy capable of behaving rationally (in the absence of a clear definition of "rationally" in this context, I would have used "predictably"), what undirected origin would suffice for a fully-formed intelligent entity with the unimaginable power and knowledge required to start (and, for a theist, maintain) a rational universe? Such an entity would be even harder to make without directed labour!
One solution to this is to posit an even more powerful entity to make the god; let's call it an uber-god. If you do this, however, the uber-god itself has to have been brought about by an uber-uber-god, and so on. An infinite regress is set in motion, and we're soon drowning in ubers.
Another solution is to posit an undirected origin for the god, or a lack of origin in the case of an eternal god. But what such solution cannot then be applied directly to the universe, eliminating the necessity of the god and making for a simpler hypothesis all round?
The origin of the universe is a profound mystery indeed. It remains so because the god hypothesis is an inadequate explanation; it requires an even grander explanation for itself, or it forces you to find a viable alternative which can then replace it.
I've answered this argument a lot on this site, but I think it deserves a summary question. My aim is make this a reference for any subsequent "origin" questions.
The Cosmological Argument or Argument from First Cause is the proper form of the common argument that the universe must have been deliberately created, and you can't get "something from nothing". It predates Christianity, as Plato and Aristotle had their own versions.
That's the first issue with the argument: it only attempts to prove the existence of a Creator. It is therefore a deist argument, so when a theist uses it to prove a specific god with no further logic it's a step too far. Keep an eye out for this.
The basic premise that everything finite requires a cause is the least controversial part, but even this isn't rock solid. Possible exceptions are found in quantum mechanics, where particles move about in a probabilistic fashion. Until observed, a particle may be anywhere in a small area, and in a sense is everywhere in the area. When you observe it, it picks one spot and stays there. This is of course a gross oversimplification, but the point is that there's no known force moving the particles around. There may actually be no cause as such, and the universe may be far more spontaneous than we think.
Even "something from nothing" is plausible according to a related theory that "nothing" is really a quantum foam from which matter may emerge. This is purely theoretical at the moment (it makes mathematical sense, but there's not much physical evidence), but it's worth remembering that science is actually considering ways like this in which matter could just pop out of "nothing". It can't be dismissed entirely.
Causality may also be irrelevant if time wasn't linear at the beginning, if it had a beginning. An effect must follow its cause, but this is meaningless if chronological order hasn't settled down yet.
The universe is widely regarded by lay people (who aren't young-earth creationists) to have begun with the Big Bang. This may seem counterintuitive - how can something be created by an explosion instead of destroyed? - but it was no ordinary explosion. All the matter and energy in the universe was compressed into a singularity, a point so small it had no volume at all. (Absurd as this sounds, it happens today with large amounts of matter in the centres of black holes.) Then it expanded outwards, and it's still expanding to this day. Once the matter was in that singularity, nothing was created or destroyed, only distrubuted.
How did the matter get in there? Was the Big Bang the true beginning, or a continuation of something else? We haven't a clue. A god is one hypothesis. Other universes, with their own separate systems of time and space, are another. The quantum foam is an outside chance. Who knows what else we haven't thought of.
I like the idea of a multiverse, an eternal group or series of universes setting each other off. It's got one up on gods because it's multiple instances of a known object. We know there's at least one universe (this one), while we don't have a single example of an established god. If you see a huge cabbage patch where the whole crop's been eaten, and you find one fat little rabbit in the corner, do you assume that Bigfoot must have done most of the damage? No, you wonder where all the other rabbits are hiding.
The theory of expansion and contraction, of many Big Bangs and Big Crunches, has fallen apart recently with the discovery that the expansion of the universe is apparently accelerating. That means it will never return to the singularity, and it is not cyclical in the way we thought. That doesn't stop it from being cyclical in other ways, for example stretching until it tears a hole and then draining out to somewhere else.
The point is that if you do accept that everything finite must have a cause, something must be eternal. Either it's the universe/multiverse, or it's a god. There are many theories, and potentially many more, which allow for an eternal universe which needs no cause. Therefore an eternal god is not the only option, and anything which says so is a poor attempted proof of its existence.
Note: The argument that a god created the universe based on the universe's nature, order, awesomeness, etc. is not related to causality. It's the Argument from Design, which is next on the GBA hitlist.