Is there a formal name for this statistical fallacy? "Given the infinite amount of possible configuration of the universe and the fact that if something in the universe were slightly different, we wouldn't exist, we can conclude that it couldn't (or probably could not) be created by the randomness".
It's such a common argument when someone tries to argue the necessity of a rational and active agent creator for the universe that it we see it in an Sheldon's series episode. But is not hard to notice that it's a statistical fallacy exactly like that one:
Suppose I threw randomly a dart in a circle and it hit exactly at the point (3, 4), if one says for me: "There infinity many points you could hit, so, if you threw it randomly, the probability (using the limit definition) of you hitting that point is 0, therefore you didn't throw it randomly and must have something external being that rationally made this dart hit (3,4)".
In this kind of fallacy we assume that a certain state in a sample space should have a high probability to be random because it's arbitrarily labeled as "special", but, in any continuous distribution, by definition, all possible states would have a probability equals 0.
Is that a known fallacy in the formal stats world? If so, does it have a name?

The Fallacy is not statistical. It is related to determinism. old science was deterministic and also stiff . So the butterfly effect was a logical consequence: you change something just a little bit and the future is completely different as a result.
This is not how science is understood today. Determinism is gone, and even In stiff systems we are finding attractors. In other words, today we should easily envision that small changes do not matter. You step on a butterfly in the past, come back to today and see the world is indistinguishable the same. OR you go back to past , don’t kill a butterfly but when you come back the world is completely different because it is not deterministic. Every time you run it, you get a different result.
The world is robust to disturbances, at least to some of them, because it is also non deterministic
