The Big Bang was the cosmological event that started the Universe.
The Universe started its existence in an extremely hot and dense state, and it expanded from there to the present day, with its expansion continuing. The more recent phases of the Universe's expansion are reasonably well-understood, like the nucleosynthesis era from 3 to 20 minutes. Not surprisingly, the earlier phases are much less well-understood, though some plausible hypotheses have emerged, like inflation.
Cosmological inflation is a period of exponential expansion where the Universe expanded by a factor of 2 or so every 10^(-36) seconds. Inflation flattened out the Universe and froze into place quantum fluctuations as they got stretched beyond the horizon size. The flattening solves the "flatness problem". The Universe's mass density is very close to the critical density for its expansion, the boundary between an eventually-collapsing Universe and a perpetually-expanding Universe. Early in the Universe's history, it would have been much closer. This is sometimes cited as evidence of fine tuning, but inflationary cosmology can explain it without requiring fine tuning. Inflation can also explain the spectrum of primordial fluctuations, making it supported by more than flatness.
What happened before inflation is a more speculative issue, with a common speculation being origin from a quantum fluctuation. An alternative, which may not be mutually exclusive, is that our Universe is a bubble in a multiverse, one of many such problems.
Some Christian and Jewish apologists have claimed that the Big Bang was when God had created the Universe, and some of them go further to claim that Big-Bang cosmology supports Genesis 1 and "Let there be light". However, Genesis 1 pictured light in a dark Universe, rather than a primordial fireball/explosion.
Georges Lemaître, a physicist who helped develop the Big Bang theory, had been a Catholic priest, but another physicist who had done so, George Gamow, had been an atheist (Gamow, George and Edward Teller - GWUEncyc), and most other atheists have had no philosophical difficulty with the Big Bang theory, even those who have preferred other cosmological theories. An exception is Huascar Terra do Valle who had asked Is the Big-Bang a Religious Hoax?. Terra do Valle made the mistake that another freethinker had done. Around 1750, Voltaire had debunked fossils, claiming that they were travelers' leftovers and the like. That was likely because they had seemed like great evidence of Noah's Flood (RE: Voltaire and fossils).
A "God of the Big Bang" has an additional problem: it seems almost impossibly distant compared to the gods of traditional theologies.