Despite the scarcity of sensory input during sleep, dreams don't really arise from nothing. They do, in actual fact, arise from the following something: memories and imagination (the latter often stemming from all sorts of associations between concepts and schemas that the brain has already been exposed to).
So I don't really see how the analogy fits. In fact, genetic information even precedes the individual by millions of years. As for answering the "how" version of the question, at the moment, we can only come up with plausible quantum mechanical theories - you better believe quantum fluctuations were involved at the beginning anyway - and a better grasp of the way the quantum realm behaves will help to reduce uncertainty.
There was definitely something like a Big Bang (there is solid evidence for this) but it might also have been a Big Bounce in a multiverse. It is possible, as I've mentioned before, that the real beginning happened so long ago that all traces of it are long gone. We may never know the real answer to the question or in the least I have a funny feeling that it may elude us for longer than the mystery of consciousness.[ Post made via Android ]