It's not often that I agree with Swing_voter, but he has a point.
Using terms of art a bit loosely, in an infinite system there is no singularity. You get only an infinite number or zero. While we may or may not live in an infinite system, it serves as an approximation in most cases. We know we exist, so there should be an infinite number of beings enough like us to be treated as a class. That is not what we observe, which is suggestive of an intervening agency. By Occam's razor, there is a creator.
The logic is sound. The assumptions require close examination, but they are at least workable. It is most easily attacked by two routes. First, the universe may not be infinite, merely large enough to seem so. Bounded systems allow singularity. The other is that our observational powers are inadequate to the task. Either way, the suggestion of outside intervention is plausible.
To me, Fermi's paradox is sufficient proof that we are indeed alone on the mortal realm. On a time scale of billions of years, beings like us would populate everything remotely habitable. Even if they had come and gone, we would find detritus.
He did.