The "we are the first" argument seemed less convincing than it could have been. A better argument from that perspective is the observation that Type III civilizations expand at an alarming rate. Whatever the motivation for expansion[1], basic simulations and back of the envelope calculations show that even with technology we could imagine building in the not so distant future, humans could expand into the cosmos at >0.9c. We must assume the same of ET.

Now information only reaches us at the speed of light; we are only capable of looking for ET in our own past light cone. That means that any Type I or Type II civilization like us should expect to see an empty sky for most of their existence, until all of a sudden the most distant stars go dim (Dyson sphere, or whatever energy capturing device). And the darkness spreads in a wavefront travelling at almost the speed of light, until it hits and ... the unpredictable happens.

We see an empty sky because if the sky wasn't empty, the planet we call Earth and our Sun would already be consumed by some extraterrestrial Type III civilization and Fermi would never have existed.

[1] An inflationary universe provides incentive for a hypothetical Type III civilization to spread throughout the cosmos as quickly as possible, as idle time means regions of the universe becoming permanently inaccessible. Or maybe just resource competition and a desire for some elements of a population to remain on the frontier.