Imagine two speeding supersonic jets randomly flying through the air, around the world, with two passengers (one on each) blindfolded and told to, at any random point, remove their blindfolds and look for the other jet. How likely is it that both passengers would remove their blindfolds at exactly the moment necessary to see each other at the same time? Indeed, how likely are they to even see the other at all, even if one or the other was blindfolded?
This is what I believe to be the #1 dilemma of the whole alien contact paradox. Our one Universe is roughly 13.5 billion years old. Humans as a species have only existed for about an infinitesimally brief period in that time. Human civilization? In cosmic terms, that's about a split second.
So, in following the above analogy, how likely is it that, across the vast distances of even our own galaxy, let alone the entire universe, that another civilization would just happen to evolve as a species, attain civilization and advance to the point where they could (or would want to) contact us within that tiny window of time?
It's almost statistically impossible.
We're likely dealing with, as an extremely liberal estimate, margins of millions of years. Every human on Earth is more likely to win the lottery several times over than we are to be visited by these aliens with extremely convenient timing. Such calculations are based on nothing more than basic logic and rational analysis. Believing that we have been contacted or that there are aliens observing us then enters the realm of speculative, unsubstantiated certitude, or faith.