One thing which is important to remember is that the Big Bang theory is a mathematical model that fits in with physical observations and helps with predictions. The model is beneficial in that it's both useful and intuitive. However, there might be many more models, possibly more complex, or simpler, which would do the same job. Saying we know that a Big Bang occurred is thus a shorthand for saying "for our intents and purposes, it's good enough to assume that a Big Bang occurred." However, although it's good enough for cosmological study, it's obviously not good enough for individual predictions, i.e. which code of conduct will lead to the highest form of welfare. For this purpose, empirical science has found its way into the field of psychology, which is, unfortunately, notoriously lacking.
The Buddha's Dhamma includes such a code of conduct, and certain cosmological references, but always in terms of the individual, e.g. what gives birth to our experience of the world, what sorts of possibilities are there to experience, what sort of conduct leads to each, etc.
Though the Buddha recalled past lives from, to quote, "many eons of cosmic expansion and contraction," he didn't present (in the suttas) any clear-cut genesis story. There is one sutta where he talks of how worlds of experience are generated, but never in terms of the origination of "what's out there." Nor did he take a stance on whether things have an inherent existence or not.
You'll find many interpretations of the Buddha's statements about the world. For instance, when he describes an "intergalactic void with a darkness beyond any other," it correlates with black holes. When he speaks of other realms of existence, it correlates with other galaxies, or (considering recent cosmological theories) universes. When he talks of beings who are invisible to the ordinary human eye, it correlates with the theory of dark matter. But it's crucial to note that these are all worthless speculations, which might or might not have anything to do with his intentions. They have nothing to do with the tasks he left us with.
It's useful to note how, even though infinitesimally few people have been on the moon, us lay men and women always want to hear more about the size of the universe. When we think of the solar system, we're awed; the milky way, woah; the observable universe, and now the multiverse theory, we just can't get enough. If and when multiverse becomes a standard belief, we're going to watch out for bigger revelations. All of this to feed out insatiable intellect. Regardless of whether the size and origination of the universe is of any importance to us, we can clearly see why the Buddha, even if he knew about it, would not even spare a taste if it didn't directly support his path of practice, which is said to be the path to end the craving for existence and thus the end of all of our stress and suffering.
Hence, Science and Buddhism are not in competition. We study science for certain purposes. We practice Buddhism for others, such as to set clear boundaries for ourselves so our minds don't get carried away with ideas and sensations. In doing so, he implied we'll be able to find out the truth about many things. But that in itself wasn't the basis for his message - one which he said we urgently needed to hear.