There are an infinite amount of natural numbers, but if you count properly you'll never pass a number twice.
Indeed, however, counting is linear while the universe is more likely random. Assuming the universe is indeed infinite and completely random, there ought to be an individual with the exact same configuration of particles (including the brain) which means at some point you would have an individual with the exact same memories, position and thoughts as you at one point in your life.
However, I suppose it depends on your definition of "your consciousness". Does it requires to be continuous to still be yourself (never interrupted) or would you consider the mere replication of a state of your consciousness to be reincarnation?
I would personally say it requires to be continuous consciousness where this consciousness would stay after death and move on to become another "live" being to be called "reincarnation". (Under the more traditional definition of reincarnation where your consciousness returns into a new shell)
Unless there's an unlikely case where, for example:
The electrons in our brain interfere with something not yet detectable with our technology and it creates interferences into this "fabric like thing" that is vaguely interacting with the known physical universe, interferences which would be what we could call a consciousness (and this "consciousness" would interfere with currents in our brain and could survive the death of a creature and attach to another one being formed.) Effectively emulating surviving consciousness and reincarnation (with loss of memory)[/quote]
then I guess reincarnation is unlikely with the traditional definition.
So instead of debating things that cannot be verified just like this made up scenario, why not write some science-fiction with similar contents where people discover how to interact with it and find ways to literally blast to bits your consciousness opening a new era of weaponry, politics and conflicts, all for our own entertainment of course?
We are only sure of being conscious for as long as our brain does not die out. Why not enjoy that until those questions about the afterlife answers themselves when the time comes?