Is ours the first universe? I see here that after a very long time into the future, "Estimated time for random quantum fluctuations to generate a new Big Bang".

This begs the question, do we speculate that our big bang was the first?  Or are we one of many in a never ending chain?  Or do I miss the point entirely (being ignorant in the subject)?
It is very hard to tell whether we are in a unique Universe. The difficulty is the closer we attempt to probe in the fractions of a nano second after the Big Bang our current forumlations of Gravity and the three our fundamental forces do not work. So it is very hard to tell whether our Universe is unique. 

However, with all that said, my own personal belief is that our Universe is not unique. The estimated time for random quantum fluctuations to generate a new Big Bang as quoted in the page that you have referred to is an UNIMAGINELY large time scale. 

My question I will pose back to you is, how could we ever tell we are a unique Universe, or part of a collection of Universes?