On the subject of matter appearing from nothing, this is not what bing bang theory states. First of all, according to Einstein's famous equation E=mc2, matter equals energy. So matter can originate from energy, and energy can originate from matter (which is qhat makes nuclear fission possible). Now, in the classical theory the universe is thought to be energy neutral, which means that in essence it is also matter neutral.
Now, where did matter come from? The example of virtual particles has already been mentioned. This has been experimentally observed, where within a vacuum (i.e. an energy and matter neutral space), particle of matter and anit-matter have appeared. It is not that difficult to imagine a slight imbalance in this process, giving large quantities of one of the two. Why this imbalance would appear is the stuff of fundamental physics, but it is interesting to note that the result of this theory was that there had to be a small inhomogeneity in the cosmic background radiation. This effect was later indeed observed, AFTER the prediction. The power of science in action.
You can accept it or not, but the presence of matter is the least of the Bing Bang's problems. The major one is the incompatability of the Quantum Mechanics with General Relativity.