What is the Big Bang Theory and does it relate to how the universe came into existence?
The Theory explains the observations of an expanding Universe and the background radiation. It explains how the present Universe came into existence but not the origin of matter/energy.
Edwin Hubble observed in the early 1900s that the Universe exhibited a marked red shift. Objects that have a red doppler shift are moving away from the observer. This lead to the conclusion that the Universe was expanding.
The Big Bang was developed to explain the observations of a an expanding Universe that appeared to have a beginning. The idea was that the all the matter and energy of the Universe was contained in an unstable superdense ball of matter. The ball exploded sending matter and energy in all directions creating our present universe.
The Big Bang does not explain where the superdense ball of matter and energy came from. The popular theory that the Universe alternated between big bangs and big crushes has been disproved by the evidence of the increasing rate of expansion of the Universe.
The Big Bang answers the question of how the present Universe came into existence but not where the Universe came from. The idea that the present universe is the result of alternating cycles of expansion and contraction has been disproven by the supernova studies that show the rate of expansion of the universe is increasing. This means that is impossible for the universe to recycle increasing the mystery of where the big band came from.