When the material being formed in the Big Bang began (from an infinitely small and hot point), the dimensions of space-time came into being. Before that time simply did not exist, at least not in our universe. So the answer is that nothing could have existed BEFORE the big Bang, because there was no time in existence "then" for it to happen in.
This raises the important (religious) question about what caused it all to happen at that moment, and although I am no big authority on these things, it seems to me that it was caused by an agency living in a separate universe, whom we sometimes claim to be God. He must have created the 3 space-like and one time-like dimensions (and possibly another 6 or 7 more tiny ones, as seen in the developments of String-Theory), the speed of light and all the other basic physical properties of our universe, which today are commonly expressed by the Laws of Physics and Chemistry, etc.