In my opinion the odds are the BB was in fact the "Beginning" of
time. We cannot say for sure and may never be able to say for sure,
unless of course someone demonstrates an alternative history to have
been true.
The thing to do when thinking about infinity is to avoid that word and
use instead "endless." It helps avoid the mistake of thinking of
infinity as a number -- some place in the very very distant past -- and
realize that if time is endless then there cannot be a "now." You can
climb out of a well that has a bottom, but you cannot climb out of a
well that has no bottom.
If time had a beginning, then talking about "before" that beginning is
nonsense. There was no existence "before," no "eternity" as there was
no time to have an eternity. There was also no causation: if something
happened -- anything might happen -- that would be the beginning of time
and after that you can insist on cause and effect (although I don't
think causation is quite as real as we think it is, for this issue it
doesn't matter).
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