See, the things we're talking about here are so immensely unlikely that it's pretty much impossible. Firstly, I don't know of any universe models that permit the beginning to be infinitely in the past and the ending to also be infinitely into the future. This permits a never dying universe, which would hold that it was perfect. This blatantly flies in the face of the decaying universe, a theory that has all but been confirmed by modern science, and the big bang theory, which is in a similar state of near perfect evidence. This means that at some point there was less matter (in a universal state that allowed for such a breaking of the laws of physics, such as the state of nothing that must have been BEFORE the universe, or before existence). The decaying universe insinuates the eventuality of a time where there will be no universe at all, and therefore no matter to rearrange itself.
Now, in the universe's limited life, is it possible that the exact same atoms could make up the exact same thing two times in the same place so as to facilitate a human being like yourself? Theoretically yes, but practically it is impossible to confirm or deny, delegating this proposition into the realm of un-falsifiable hypotheses and thought experiments (such as the existence of god) that cannot be touched by science, because it is un-testable and un-confirmable.
And your answer to the question about whether this clone would be you is determined quite wholly on your belief or lack of belief in souls or the infinite nature of the human spirit. Technically, if you believe in such things, your spirit would have to be imparted into this clone, otherwise it be merely a golem with your looks. One other thing worth noting may be the fact that this creature, whatever you may call it, could have different experiences, and even if it should be you wholly, it's own cells would be manifest of different atoms until it was, technically, made up of other parts of the universe you were not. We are all the products of our interactions, both figuratively and very literally. Finally, note that this creature would also exist at a different time, making it easy to distinguish between the two of you historically speaking.
So, TL;DR yes it's possible, but it's highly unlikely. And no, for a few reasons, it would not TRULY be you.
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