We observe that violent activity occurs constantly on Earth and in the Cosmos as a whole, and all is entirely attributable to the laws of physics - as it has been since the first moments of the Big Bang - and the laws of physics pay no heed to our regard of them. We exist because of them, and shall one day cease to exist because of them.

Needless to say, you're free to use your preferred term although, if you do, you'll still be tasked with explaining that what you really mean is Big Bang. The term Big Bang, coined by Sir Fred Hoyle, differentiates it from his own expanding universe theory - i.e. the Steady State - whereas your "Big Expansion" doesn't.
"Time is what prevents everything from happening at once" - John Wheeler