There are often heated discussions about the Big Bang. The Big Bang is well defined as the high density state that you get if you extrapolate the today observable cosmic Hubble expansion backward into the past. This definition has been the same one all along; it did not change; it is still valid today.
What does this entail?
1) The Big Bang tells you nothing about the absolute size of the universe at any time! As far as the definition is concerned, it may have been infinite all along. The Big Bang is not where the universe has zero size.
2) The Big Bang is similar (similar, not equal) to an explosion, because with an explosion, you have the fragments that are double as far away from the blast site going at double the speed - that is why they went double as far, doh! This relation between distance and speed is precisely the gist of the observed Hubble law that led to the Big Bang theory in the first place. To be sure, the term “explosion” is also misleading in many ways. One should not think that high pressure caused the explosion; pressure actually contributes to gravitational attraction.
3) The Big Bang comes after whatever led to the high density state called Big Bang. We today know that cosmic inflation led to the high density state. The Big Bang is thus best identified with so called “Reheating” after inflation.
So called “decoupling” (also “first-light”) comes later, thus the cosmic microwave background is often referred to as the “afterglow” of the Big Bang. Note that this would not make any sense at all if the Big Bang were to be put before inflation! Inflation stretches space so much, no afterglow of what was before could possibly be left.
You cannot count inflation towards the observed expansion and then claim that the Big Bang came before inflation, because the inflationary expansion is not at all what you get if you back extrapolate the today observed expansion. The Big Bang is when inflation ends and the Universe's expansion rate is dominated by matter and radiation density. The expansion of inflation is dominated by something that dear old Hubble would not have envisioned in his worst nightmares, so it cannot possibly belong to what we get by merely back extrapolating the expansion observed already in Hubble's days.
4) Inside the classical theory of general relativity, which does not know about inflation or quantum physics, the back extrapolation leads to a mathematical singularity, to infinite density. Inside the confines of the naively classical theory and right where the theory was always expected to break down anyway for the simple reason that singularities pop up (never a good thing to have un-measurable ingredients), the Big Bang would be a singularity where one cannot say what came before. Not being able to say what came before does not even here imply some sort of absolute beginning. To take this little piece of known to be wrong theory and blow it out of proportion as the physical Big Bang is no less than crackpottery.
Why is there so much confusion and heated debate about this, although the definition is reasonably clear? Well, if you have a time scale and you are working backwards, you will likely put the zero somewhere into the past and then approach it. There is no deep significance to the zero point, before which there are negative values in most scenarios. However, even atheists fight about the Big Bang basically because they cannot shake off creation myths. The Big Bang outside of science is always to do with fiery creation. And that is why we need to add this:
Inflation is not an absolute beginning either. Science does not yet know what came before inflation. There may be no more but some really boring empty space before inflation or maybe eternal inflation. Likely, the time parameter simply makes no sense anymore at some point, because time is a measure of changes; it compares processes with the processes in a “clock”, and if nothing changes and there is nothing that can serve as a clock, there is no time.