It's better to think about the Big Bang as an admission of failure: using our best stitching of the two best theories that we have about the universe, and extrapolating back the data at hand as further as we can, we arrive to a point where our description breaks down (the singularity).
Will a better theory cast a brighter light on this point in space-time? I assign a 99.9% probability that it will.
I think that only the most zealot between relativists bite the bullet that inside a black hole there's actually a point where the gravitational field reaches an infinite value. And given that the more time passes the more paradoxes we discover about black holes, I'd say that quantum gravity will revolutionize our understanding of singularities. So my probability to Big Bang actually happening is 0.1%