how is it I was born into the most intelligent species on Earth, which also happens to be the only sentient species in the known universe
What are the chances of that? Well, this can be explained quite simply: If you were not human you wouldn't be pondering the question in the first place. It is tautological. The very fact that you are human means the question has significance to you. It doesn't matter about the chances of it, you simply are.
Now, that may not sit right with you. It doesn't with me either, and in fact, it doesn't sit right with many physicists. Which is why we have 'multiverse' theories in fact.
There are two reasons for why we have multiverse theories: To solve some issues within quantum mechanics (Schrodinger's cat; a cat can be alive and dead at the same time), and to answer why we observe what appears to be a fine-tuned universe.
The idea of a fine-tuned universe is of more interest here. The universe appears to be on a knife's edge in many ways. For instance gravity is the exact strength it needs to be. It cannot be any stronger or weaker. The cosmological constant (energy density of space) is exactly what it needs to be. Cannot be stronger or weaker. Physicists have found this pattern in many things.
Now some explain it away in a similar way to how I originally did. Many others see a problem here though. Something that needs to be explained. One way to explain it is, there is a god. Not a satisfactory explanation to many in the fields of science. Another way is multiverse theories. There are possibly millions, if not an infinite number of universes popping in and out of existence. If you think of these constants as variations on a dial. Each universe has different variations of dial settings; so some have gravity that is a little bit stronger for instance. There are a finite number of settings. Because there are millions or even an infinite number of universes it is inevitable that one of those universes will have the exact settings needed for life and the universe we observe. Like an infinite number of monkeys writing the whole work of Shakespeare.
And so to return to your question: How is it possible that you exist when the odds seem so stacked against it? Perhaps because in reality it is impossible for you not to exist. If there is a possibility then it
will be expressed.