Is it fair to think about the statement "the big bang happened everywhere at once." as meaning the singularity that spawned the "big bang" was very large by cosmic scales, even infinitely large? (I am aware that the word "singularity" refers to a place where the math breaks down and not a point in space. I also am aware that "before" the big bang there was no time or space and that giving the "singularity" a spacial measurement is strange at best - but I want to pose the question nonetheless.) Another way to ask this question is if the singularity was infinite in size and the big bang was in any way comparable to a pre inflation era inflation of the singularity.