On the odds of finding life in the vastness of outer space

I’ve been thinking a lot about the scale of the universe for my own writing. Not just the distances between stars, but time itself.

Humanity has existed for a flicker of time in cosmic terms. The universe has been around for roughly 13.8 billion years. Civilizations like ours might last millennia, maybe tens or even hundreds of thousands of years.

When I imagine interstellar travel, it strikes me how unlikely it is to encounter not only a habitable planet, but one that is occupied or even shows evidence of previous life at the same moment in time in that tiny fraction of the universe that one can realistically explore. Even if life is common, civilizations may rise and fall long before another reaches their system. By the time we arrive, the planet might be empty, all traces of its inhabitants long erased.

I’m imagining an atmosphere of almost oppressive emptiness: a ship drifting alone, finding only dead, uninhabitable worlds along its path.

How do others here think about it? Do you focus on the probabilities and the rarity, or do you imagine civilizations somehow persisting long enough to meet?