Common sense necessitates a primary cause to the universe, and the so-called "First-Cause Argument" continues to stump people who ponder God and the Big Bang. Really, both God and the Big Bang are equally faulty when considered to be first-causes. In either case, the continuity of causation, which is assumed to be fundamental and timeless by nature, is contradicted by the notion of a non-created being or a non-caused event. However, "First-Cause" is not as preponderant an obstacle as we have believed it is.
Our understanding of the universe is as limited as the scope of our own intelligence, vision and imagination, so it seems entirely unlikely that our perceptions of the world are at all similar to reality, to the truly fundamental systems that affect what we observe with our limited senses. Still, we can catch glimpses of the microscopic and the celestial and use the knowledge gained from these glimpses to get closer to the truth; but what is damning about this line of study is that all our observations are local -- that is to say, we can never see beyond the causal universe of which we are part. Since everything we see appears to have been caused by something else, and in turn has an effect of some kind on something else, we hold causation to be a fundamental system of the universe. But the ubiquity of a system where you live does not make it an intrinsic part of reality as a whole. If we were born on a planet where the sky was invariably yellow, and had never seen a planet besides our own, we would make the sensible conclusion that yellowness was an intrinsic property of the sky. Any dreams of a far-away land where the sky was blue would be discarded as nonsense.
With this in mind, I posit an idea about the nature of causation: The system of cause-and-effect, which pervades our region of reality that we call the universe, is localized in said region and does not necessarily exist elsewhere in the vaster space beyond our cosmic realm.
In this possible reality, time has a very definitive nature and responsibility, which might support or defeat the possibility of such a reality depending on Quantum Mechanics' final verdict on the nature of time. In the reality posited here, time is a degree of freedom -- a temporal dimension -- catering specifically to the existence of causal systems. Causation is then a quality possessed by all things in relation to one another along this dimension: in a way similar to how gravity is exerted by massive objects in relation to one another along the fourth spatial dimension (the dimension through which the warping of space-time happens), causation is exerted by things in the universe in relation to one another along the dimension of time. As gravity is a local property of dense regions in space, so might causation be a local property of certain regions in space.
This brings up a strange conclusion about this possible reality: the universe's existence has no real cause. If causation only occurs over the localized (albeit vast) region of space that is the known universe, then the space outside the universe would be, by default, void of a causal system. We can readily observe an analog to this by noting the very fact that when we are in zero gravity, we do not notice the presence of gravity warping space via the fourth dimension, and therefore neither do we notice the presence of the fourth dimension at all. Naturally, if nothing ever moved forward to back and things only moved up, down, left and right, then we would have no concept of the third dimension, either. The same could possibly be said for time. As a dimension, time would exist everywhere but only appear to flow in regions where causation occurs; this is because causation is what generates the illusion of time's motion for sentient beings like us. (It's actually more than that; but more on this later.) Thus, temporal causation can only affect timelines that exist within the universe; and seeing as the universe's creation would lie on a timeline outside the universe itself, it stands to reason that the possibility of our universe lacking a temporal cause (i.e. a creator or genesis) is very real, indeed.
How else can we justify the universe's existence, then, if we deny ourselves all causal possibilities? The clearest answer I can come up with is that, being a spatial entity unbound by an external causal system, the universe owes its existence to some non-temporal set of physical laws, and that these laws must govern the physical and spatial patterns of all things that exist. The best candidates for these laws I deem the principles of mathematics and geometry, or possibly a subset containing some of the more holistic principles in each field.
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