The Big Bang is a major event in the history of everything, marking the beginning of our universe.
Despite this, the Nibblonian race was already 17 years old. It is unclear how this is, since the Big Bang marks the beginning of time itself (see general law of relativity), but it's possible that the Nibblonians at first dwelled in another universe and later moved to our, or that they simply over-exaggerated. Another possibility is that they came into being near the end of the universe, and used a device similar to the Professor's time machine to survive the Big Bang. According to the Nibblonians, for the first few milliseconds after the Big Bang, everything was good, but then the Brain Spawn came into existence. Since then both sides have lead unceasing war against the other.
The Professor, Fry and Bender witnessed the Big Bang on first hand, twice, in "The Late Philip J. Fry".