They are controversial for those who actually have some understanding of what the Big Bang entails. It's not an "explosion" in the conventional sense of the word.
I take it your understanding of the Big Bang is the same as Carson's?
My understanding of the universe is like many in that we dont really know. There are a lot of ideas out there but none are really proven. There are conflicts even with the most popular theories and the maths doesn't add up to say that these theories are validated. IE there isn't enough mass in the universe to hold itself up so dark energy has been hypothesized. This hasn't been verified and is still a big unanswered question which is related to how the universe started.
Another problem with the big bang theory is the problem of a flat universe and the cosmological fine tuning. Scientists have said that the universe is flat from the evidence that the background radiation emits. But to get a flat universe it would take a very fine tuned beginning with the big bang.
Flatness problem
Such problems arise from the observation that some of the initial conditions of the universe appear to be fine-tuned to very 'special' values, and that a small deviation from these values would have had massive effects on the nature of the universe at the current time.
https://en.wikipedia.org/wiki/Flatness_problem
All Carson is saying is what many have said that this is all speculation. He is asking the question how can order come from chaos.
I understand its not an explosion and more of an expansion. But that doesn't matter so much when it comes to the beginning of things being random and chaotic. It wasn't the result of a guided process that was going to place things in their order so that it produced certain fine tunings that go beyond chance happenings. I tend to lean towards there being one universe and it is fine tuned for life. I think all this speculating about parallel worlds is mainly to explain away that fine tuning and design we see in our universe.
Thats why scientists propose a multiverse where there are many parallel universes like bubbles that expand from each other. In this scenario it makes the chances of creating a just right universe for life like ours not so special. If there are many universes all having slightly different physics then chances are one of them would be like ours. Thats why I guess its a bit far fetched and controversial. Because its even debated among mainstream scientists. I think mainstream scientists are stumped by the fine tuning question and that the maths doesn't add up when taking relativity into consideration.
To say its not contested and is a consensus is a little misleading because its all speculation and nothing is proven. There are many hypothesis out there for how the universe started. The multiverse or parallel worlds theory is probably the best and most common one that scientists support nowadays. String theory is the latest theory that is derived from this. So the big bang or inflation theory is only part of how scientists think our universe started.
The Case for Parallel Universes
Another key aspect of the new worldview derives from string theory, which is at present our best candidate for the fundamental theory of nature. String theory admits an immense number of solutions describing bubble universes with diverse physical properties. The quantities we call constants of nature, such as the masses of elementary particles, Newton’s gravitational constant, and so on, take different values in different bubble types. Now combine this with the theory of inflation. Each bubble type has a certain probability to form in the inflating space. So inevitably, an unlimited number of bubbles of all possible types will be formed in the course of eternal inflation.
This picture of the universe, or
multiverse, as it is called, explains the long-standing mystery of why the constants of nature appear to be fine-tuned for the emergence of life. The reason is that intelligent observers exist only in those rare bubbles in which, by pure chance, the constants happen to be just right for life to evolve. The rest of the multiverse remains barren, but no one is there to complain about that.
http://www.scientificamerican.com/article/multiverse-the-case-for-parallel-universe/