First, the big bang may or may not be the origin of matter. Supposing it was, and accepting that matter "originated" in our Universe, the original matter certainly was not carbon. The big bang is where theoretically the universe as we understand seems to have started its current existence. "Original" matter existed on the boundary of energy and matter. Particles may have existed simultaneously in both realms. It is theorized that eventually the fundamental forces (as we understand them) arose from the forces that governed the big bang. The weak nuclear force, strong nuclear force, electromagnetic force, and the force of gravity began to apply to these massive (in the strict sense) particles leading to the formation of subatomic structures, including quarks. These subatomic structures in turn, led to the simplest of atomic structures, and so forth until stars, galaxies, and eventually the incredibly complex organic structures we call life came into existence.

Now, as far as the existence of life and its origins, Paul Davies, as well as other theorists and scientists believe that life is an inevitable development in the universe, and that self-organization is an inherent character of this universe, and that there is life everywhere whether or not we think so. Self-organization and the concepts surrounding the idea are at the forefront of modern science, in the fields of physics, biochemistry, cognitive science, modern philosophy, mathematics, and computer science. I believe that the questions being asked today are of great importance: Can existing systems spontaneously evolve into more complex, yet more efficient systems? Are there rules that govern the behavior of systems in order to drive them into higher complexity? What are these rules? Why can we accept the development of incredibly complex interactions and systems for non-living systems, but not accept that life can arise following the same universal rules that created atoms, stars, and thought?

Please keep in mind, I'm sure there are others who could tell you much more.