Logically speaking, the BIG BANG never happened, it is only a theory, this is where cosmic evolution becomes the Big Dud.
There's no evidence of a Big Bang and even put more ridiculously, the theory states that all the matter in the universe was compressed into a tiny small portion of nothing, which also negates the fact that they are taking an existing universe, compressing it, then creating a theory of decompression of the same universe which in itself is self-replicating every 80 - 100 billion years.
Each and every time that the compression was to take place a pre-existing universe was already awaiting to be compressed.
It's circular reasoning and is a weak theory on cosmic evolution and avoids answering the question to when was The begining?
The Big Bang is only a theory for expansion and contraction (Oscillation) of the universe and does not imply first cause.
One point to bear in mind is that the compression/decompression cycle you are talking about is only one conjecture about many regarding the formation of the universe, and since the universe at the moment is accelerating further outwards, it does not appear to stand up to current evidence.
There are, however, myriad other theories with absolutely no observable evidence to back them up, since all the laws of physics, and indeed time itself, only came into existence after the Big Bang.
So it is wrong to say that the Big Bang is incorrect since one interpretation of it does not hold up to scrutiny. There are many other explanations that are mathematically watertight.
In addition, as with much of science, we cannot categorically state whether the Big Bang theory is correct. However, as with all scientific theories, it is the best explanation we have at the current time based on the observable, testable evidence we have available to us.
The two main criteria we have as evidence for the Big Bang are the acceleration in expansion of the universe (as mentioned above) and the "cosmic background radiation" of the universe. The first of these was the reason for the Big Bang theory being initially proposed, and the second was the theory's greatest triumph. One of the things expected of a scientific theory is that it make testable predictions. In this case, it was expected that the rapid expansion of the universe would leave a fair amount of excess energy lying around the place. This was detected in 1965 as microwave radiation at a temperature of 2.7K (quite a lot considering it pervades the entire universe).
And I think the word you were looking for is "cosmogony". "Cosmic evolution" is a phrase used by nobody unless they wish to somehow debunk evolution and the Big Bang is one go, which, considering the two are completely seperate theories in utterly different branches of science, is not going to be possible.