>I am curious to know what could disprove The Big Bang or Abiogensis.
Abiogenesis would be very difficult to disprove. About the only way to do so would be if we had extraterrestrial fossils proving that relatively complex life already existed within a VERY short time after it first COULD have existed (we're talking, like, under a million years here, to be realistic). Alternatively, if it could somehow be shown that the simplest life forms capable of surviving in an otherwise lifeless environment are also relatively complex. However the current state of scientific understanding suggests that both of these are extremely unlikely. Furthermore, they would still not prove the existence of God, all they would show is that the life in our universe probably traces itself back to some other universe.
The Big Bang is somewhat easier to disprove. All it would really take is for whatever mathematical/physical model that best explains observed phenomena about the Universe on a large scale to be of a nature that shows the Big Bang can't have happened. What such a model would be like I don't know, but we nevertheless have to be prepared for the development of such a theory just in case it does come along at some point.
>I know that proving a 'creator' exists is impossible by design
Not really. It might be fairly hard, but it's not impossible. What IS impossible, at least within the realm of empirical science, is to prove that a creator does NOT exist. I mean, how can you tell that the entire Universe wasn't created five minutes ago, with all life and all human memories and so on all intact, and that your memory of living for years is really just an illusion? You can't. Unfortunately, a lot of people either don't understand this or don't understand its implications, because I've seen people using arguments (especially to support creationism) that this principle renders invalid.
>but equally so can the scienctific theory of creation be disproven
Not with 100% certainty. Although most scientific evidence currently available suggests that YEC is not a good explanation for the formation of the world and the life that exists on it, as I mentioned above it is of such a nature that you can always keep claiming it could have happened. All those fossils in the ground? They support evolutionary theory and the 4.5 billion year age of the Earth enormously, but that doesn't mean God (or aliens, or whatever might have created us) couldn't have made the Earth with fake fossils already planted in the rock. And in fact, this is again an argument that I have seen some creationists use.