The Big Bang theory provides cogent evidence that time, space, energy and matter all began to exist at a point some 13.7 billion years ago. It seems to me that any explanation for an effect must be sufficient to explain the effect. In the case of the universe, since matter, energy, time and space all began to exist at the Big Bang, these cannot form any part of the explanation for why it happened, so that consideration seems to point towards a timeless, immaterial, non-spacial explanation.
How do those remaining “qualities” serve as proof against God, who is considered to be the eternal (timeless) boundless spirit (immaterial and non-spacial) who willed the universe into existence ex nihilo (from nothing, i.e., from no pre-existing material)? Most philosophers and scientists would concede that standard Big Bang cosmology tends toward being supportive of theistic claims rather than against them.
I am not clear why you believe Big Bang is evidence against the existence of God.