Dr. Cox will be relieved to know that in one way at least he floats Naomi's boat.
The answer, questioner, is of course "Yes": we no longer need supernatural explanations of the world. To quote Khandro's mate Nietzsche "God is dead". The intellectual argument is won. What remains is to overcome the inertia of thousands of years of social and religious conditioning and to wrest the moral domain away from the priests and idolaters where it has been so poorly served. I was optimistic when I was younger that these difficult tasks were achievable. Now, considering the triumph of Christianity in the Roman Empire and its stultifying effects on human progress for the next thousand years and the recent rise of the most ignorant and morally stunted kinds of Islamic fundamentalism, I am far more gloomy.
Re "what caused the big bang?" I've recently read Krauss's fascinating Universe from Nothing with the mixture of awe, astonishment and incomprehension I have whenever I get within a parsec of Schrodinger, Heisenberg etc. It will appeal to the more scientifically orientated.