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The term Big Bang is misleading.
It's implies explosion but the parallel is inappropriate and borders on useless.
We have a starting point for time and space which we can not describe and deal with the evolution of the Universe which inflated at at rate many times the rate of an explosion .
As Steven said inflation and expansion are separate matters. One is too grand to be called explosion and the other too humble to be called an explosion.
I think it is wise to remember we may not be describing reality but what we do describe is scientific theories which provide a very reasonable footing.
I personally find Inflation impossible to accept but I don't have an alternative theory.
My point is if one wishes to offer alternative cosmology one must offer a better theory.
As cosmology turns on general relativity one needs to offer something that takes us further than general relativity.
That won't be easy.
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