By definition there has to be a first intergalactic civilization, if there is to be at least one.

The universe is ~15B years old, and we expect it to keep forming stars (as good as any of a metric for “hospitable to life”) for another trillion years. In other words, we’re in the first percent or so of the lifespan of the universe.

Doesn’t seem too crazy that if we start conquering the stars, we might be the first ever species to do so.

(And if history is any indication, we’ll probably cause some sort of galactic global warming in the process, that all starfaring species after us will curse us for)