You are incorrect. There is no concept of time or space "before" the Big Bang; I say "before" in quotes because there is no "before" the Big Bang.
In the earliest part of the Big Bang time did exist. The Big Bang created time.
In the earliest part of the Big Bang time did exist. The Big Bang created time.
Edit:
In the early universe, before the plank epoch when we had particles of plank length or less, you know, things with a schwarzschild radius? The entire universe made of things that are black holes, nothing but black holes? Those time-ending particles that disappeared in their own hawking radiation? The first early 10^−43 seconds, where time didn't actually exist? Those were the good old days.
If time didn't exist, then how did the universe know when those 10^-43 seconds were up?
Seriously, I think this discussion is proceeding at a level which probably shouldn't be attempted by non-cosmologists. We all probably have a bunch of misconceptions we've picked up from popularizations about the Big Bang, and would only embarrass ourselves if any cosmologists happen to show up.