A pulsing motion of what sort, and how tightly do you draw a line around 'big bang'? We can see by direct observation that things have been continually getting further apart for the past 13-odd billion years or so, and the earliest thing we can see is consistent with there not being a whole lot of structure before then.

Even if the behavior in the very beginning is different than we usually expect, that seems like a big bang to me.

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%

That there was a finite time in the past in which all matter was squeezed tight and hot enough to undergo primordial nuclear reactions, and that the universe has expanded since, is pretty dang incontrovertible at this point. The nature of that event is still up for debate. Examining the fine details of light of different ages continues to reveal things, like the expansion appearing to initially slow followed by accelerating which is currently best explained by a dark energy model which is also favored for reasons relating to physical models of space I am unprepared to examine.