There is no reason to deny the Big Bang. Even though the theory is based upon certain assumptions, it is our best scientific theory so far that explains certain observations. There also exists counter-evidence and unexplained phenomena, however, until the time that we have more data that confirms or falsifies the Big Bang model, we have no other choice but to assume the Big Bang model to be correct while we allow the scientists to make further discoveries.
What is important to understand though is that the Big Bang theory presupposes the laws of Physics and attempts to explain the origin of the content of this universe (matter, energy, etc.). It does not even attempt to explain the existence or the cause of the universe. Religion, on the other hand, explains the cause of the universe and the reason for its existence so there is no overlap between the two.
The next thing that must be appreciated is that since certain assumptions have been made in the Big Bang model, any implications of the model should not be considered as conclusive truths until those assumptions themselves have been reasonably validated. Additionally, in order to assert any conclusive truths on the basis of the theory, we will have to scientifically explain any counter evidence and related unexplained phenomena. Without such explanations, it is ignorant to make any big claims on its basis such as the denial of God.
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