@Cathain phil,
To expand on the above - We can say one of two things about the Physical Universe (Plato's Sensible Realm):_
i) That is it infinite
ii) That it is finite
First we have to clarify what we mean when we talk of the "universe".
It makes sense to be describing the one which we inhabit, as this is where the OP is describing such events occuring.
So, if we take the first proposition then we are claiming the quality of infinity for this universe. The first issue we encounter is that this contradicts current scientific opinion. If there was a Big Bang, then we have a starting point for this universe - a beginning. If we have a beginning them we immediately have a contradiction with this first proposition, because what is infinite is without beginning or end. If we have a beginning to the universe then we rule out the possibility of it beng infinite. So if we are going with this claim, we are necessarily rejecting the current scientific model. As such, we would be required to offer some sort of proof to back up this rejection.
If we take the second claim, that the universe is finite (it has a beginning and/or end) then there is not an infinte amount of time to create people over and over again (or "roll the dice" as it was phrased above).
There is an added objection to the scenario as a whole - whch is the suggestion that God operates within the constrains of time, which is a quality of the physical universe. Most religions and philosophies hold God to be a transcendent being. Indeed it is logical to suppose this if we believe that this God is the creator of our universe. If he created it, then he preceeds the universe. As time is a component of the universe (Relativity holds space and time to be the same thing - space-time), then a creator has existed not only "before" time came into existence, but therefore he exists outwith time (as he exists outwith our universe).
Thus God is eternal because he exists outside of the realm of time (our universe). Eternity is the condition where there is an absence of time.
It is incorrect to think of eternity as an infinite future. It is the
absence of future or past as both of these belong to time. With eternity, these conditions are nonsensical. There is only ever the present. Plato described the difference as that of
Being and
Becoming. In the Intelligible Realm (the eternal realm) things simply are. We cannot even really say they have always been and always will, because this again is a temoral perspective.
There is no "always has been" or "always will be", there only ever "is" or "being".
The Sensible Realm (the temporal, physical universe) is the world of Becoming. Things, as Heraclitus observed, are always in flux - always changing. You are not the same person you were a second ago. The atoms & molecules in your body have altered, you have included new memories and experiences, you have perhaps forgot something. We, like everything else in the universe, are constantly changing and thus never Being but alays Becoming something else.
I say therefore, that infinity is a quality that belongs to eternity, and not something native to our universe. It belongs to the other, that is whatever is outwith our universe. Ours is a universe with limits - spacial limits, temporal limits. It is a finite unverse with a beginning and presumably an end.