There is a vast array of things discovered that refute the Big Bang Theory. Among these include the cosmic web, the First Law Of Thermodynamics, and the angular velocities of elliptical galaxies, etc. While many scientists who reject the Big Bang Theory also deny a creator, the Big Bang Theory, a philosophy I do not adhere to, actually supports the existence of a creator.
The Big Bang Theory implies that the universe had a beginning. The mere fact of entropy provides scientific support for the universe being finite in it's age. The Kalam Cosmological Argument states that if something has a beginning, then it has a cause. Since the universe has a beginning according to the Big Bang Theory, it implies that the universe has a cause.
Many people who endorse the Big Bang Theory wonder what was around before the Big Bang. Some people will argue, "If God made the universe then who made God? Did God make himself?". For something to make itself exist would imply it had to exist before it ever existed. It would therefore have to exist and not exist at the same time. This is impossible and therefore God did not create himself. Something creating itself is a contradiction to Aristotle's Law Of Non-Contradiction. Therefore there had to be something in the beginning because if there was nothing to begin with there would be nothing in existence now.
Since there always had to be something, a creationist would argue that that something that has always existed is God and that he has never not been. This is corroborated in the Bible when God tells Moses "I AM" in Exodus 3:14 and in Revelations 4:8 referring to God: "which was, and is, and is to come". An atheist denying the existence of God cannot therefore believe in the Big Bang Theory, since it suggests a beginning for the universe. Nevertheless, there always had to be something in existence for the universe to exist now.
Just as a creationist believes in the eternal existence of God, and atheist would have to believe in the eternal existence of the universe since a beginning to the universe implies the existence of a deity. An alternative cosmology to the Big Bang Theory is the Steady State Theory which was derived in 1948 due to inconsistencies in the Big Bang Theory. It claims that the universe is virtually unchanging over time. This theory was discounted in 1965 with the discovery of the cosmic microwave background radiation.
The fact of the matter is, while being a rejected view, it does not imply a beginning for the universe as it implies a universe existing without a cause. Therefore the Steady State Theory is the logical alternative to the Big Bang Theory, for an atheist, despite it's fallacy since it doesn't hold up to scientific scrutiny.
References:
1. Flandern, Tom Van. The Top 30 Problems with the Big Bang, Infinite Energy (2002) volume 8, issue 46, pages 10 – 15.
2. http://en.wikipedia.org/wiki/Kalam_cosmological_argument
3. http://plato.stanford.edu/entries/aristotle-noncontradiction/
4. http://en.wikipedia.org/wiki/Steady_State_theory
5. R. C. Sproul (tape of the month - September, 2005)