Are aliens among us? Are they in contact with humanity? Given the structural considerations, by a large margin probably not. I’ll be the first to admit the limitations of human comprehension and technology. Perhaps the speed of light isn’t an absolute maximum. Maybe something like warp speed or star gates is entirely possible. But returning from the realm of fiction and speculation, we must work with what we have. Let’s run the numbers.
From wikipedia, the Milky Way is “100,000–120,000 light-years in diameter containing 200–400 billion stars”. Let’s say 300 billion. Let’s further estimate that 1 in 100 has an earth like solar system warranting exploration. This may be optimistic, but it is balanced by the further decreased likelihood of interstellar intelligence developing when there are fewer. Data based on the Kepler space telescope suggests that there may be 2 billion earth like planets. Let’s round it and say there are 3 billion star systems worth exploring, 1 in 100.
Let’s say it takes 10 years to hop between solar systems. Given our current state of knowledge this is extremely optimistic. Even at this rate it requires 30 billion years to explore every solar system in the milky way. Granted it’s one at a time. But given the resources likely required to support interstellar travel, I think it’s a fine starting point.
The galaxy is only 13.2 billion years old. Given what I already consider to be optimistic calculations, it wouldn’t even be possible to explore every solar system in that time. We’re short by 17 billion years. This alien species has covered less than half. Moreover, you must account for the time it takes a species to develop interstellar capabilities. If they developed it at the halfway point, they’ve only had 6.6 billion years of exploration available to them and covered just a fifth. As a point of comparison, Sol is only 4.5 billion years old.
Let’s say this alien species is busting ass and will cover the entire solar system in that 6.6 billion years. They would still have had to reach our solar system in approximately the past 5000 years to encounter civilized life or in the past 4 million to encounter hominids. Taking 4 million for the hominids, that’s a window of 0.06% of their total 6.6 billion years to encounter earth. If they’ve already swung by, it’s, well, astronomically more likely they missed us.