The way I've heard this describes is with an analogy. If you have an infinite number of decks of cards, shuffled randomly, the same shufflings will show up an infinite number of times. There are only so many ways to put together an infinite number of particles, do the shufflings get reused.
You don't. There are bounds on how much matter can be contained within your past light cone before it turns out you are simply in a black hole.
The number of possible past light cones that could originate from the same Big Bang using reasonable assumptions about QM is staggeringly large, but nevertheless, finite.
