I will explain again.
''Time beginning with the Big Bang is not necessary'', as was in your own words, is wrong. If we are agreeing we are working with the standard model of cosmology, i.e. big bang, then we are talking about a theory which must encorporate time. If you want me to give you some examples of why, i will.
In this specific case it must also mean everything expanded from some point in spacetime that was smaller than a proton. The state of infinity density could be given as:
[latex]f(x)= 1 / x[/latex]
That is simply an algebraic solution to a singularity, but in relativity, involves many mathematical changes and formulations that i do not know of myself. Relativity indicates the existence of time through the presence of matter, and matter is the presence of curvature in space, which is the same as time itself, and they are found to be co-dependent as the same entities.
Thus the beginning of any big bang which involved energy, or mass, or the form of spatial freedom, it is found synonymous to the simultaneous existence of time.