Firstly, ar eyou a physicist? Have you studied in detail quantum mechanics? If not, you probably don't know enough to be able to make such sweeping statements.
You don't need very deep understanding for the statement.
If you don't believe that there is something special that makes our big bang unique (like a God who created only one big bang which would be a nonrandom factor), you get an infinitive amount of big bangs if you believe in an infinitive amount of time.
We know that there is some chance that a big brain creates humans like us.
If you get enough big bangs you will get one that recreates everyone sometime in the future (and also in the past but that is another matter). Infinitive are enough.
Secondly, if there is no soul, what exactly si reincarnated? if we are only the body, yet you believe in reincarnation, well there is nothing to be re-incarnated.
Do you believe in life before death?
If you wait long enough you get everything reincarnated that was there before death in some future point.