There is a rather nice story about this which I rather enjoyed at university. Here goes...
It was worked out by a team at Princeton in the 1960s that "if the Big Bang is true, then we should still be able to see the echoes, and by now, the radiation will have been stretched out because of the expanding universe so it should be detectable as microwave radio. Let's look for it!" At about the same time, two radio astronomers at Bell Labs in NJ, Arno Penzias and Robert Wilson, were having trouble with their telescope. Wherever they pointed it, there was this microwave hiss - now if it's coming from every direction, your first thought is going to be it must be something wrong with the telescope. They did everything, they cleaned it out thoroughly, removed quantities of what they described in their scientific paper later as "a white dielectric material" (yeah right, what they meant was bird poop) and it STILL wouldn't go away. WTF is going on?
A mutual friend put the two teams in touch and they put two and two together. The Princeton guys realised that not only were they right about this "echo of the Big Bang" radiation, but Penzias and Wilson had actually FOUND it by accident! Both teams published papers about their side of the story in the same issue of the Physical Review, and rather pleasingly, some years later they all shared a Nobel Prize.
So there you go - the light DOES exist but the wavelength has been stretched out so much by now that it appears to be microwave radio.
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Jorge Eliecer say: Yes, we actually can "see" the Big Bang, through something called Cosmic Microwave Background Radiation.
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Nyx say: The "Big Bang", doesn't have a center, since the universe formed - everywhere.
Plus, the early universe was way too hot for light to escape. That took place several thousand years after the fact, when the early universe finally cooled off enough for light to escape.