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I've also heard that all the matter in the universe was in one small grouping which exploded. The latter is makes more sense, but where did the other idea come from? Which one is more commonly accepted?
First of all, at the inception of our universe there was nothing but time, space, and energy. Later, as the energy was spread over a larger, expanding universe, matter condensed as the temperature decreased. Einstein laid down the groundwork for this theory with his equation E=mc^2. Through math, he was able to show that matter and energy can become one another in certain situations. In the seconds after the "Big Bang" it was simply too hot for matter to form. Therefore, claiming that the universe started as a grouping of matter is not accurate, it was a small area with high temperatures and high energy content.
And how do we "know" (tentatively) this? All observations of the universe support the theory that all of the mass of the universe is moving away from a central point. Therefore, all mass must have originated from that central point. If that central point were small enough in diameter, then matter could not have existed in such a small space, only energy could exist in such an environment.
What happened before the Big Bang? This is like asking what your thoughts were before your conception. It is not something that the human mind can comprehend, but may, in the future, be modelled through physics and math.