I think so. Not that long ago, humans spread across the world, first organically, then intentionally. We're at the infancy of spaceflight at the moment, the equivalent of putting food and water in a raft to go to the next island over.

We'll see humans on Mars in our lifetime, like the previous generation saw humans on the moon. Assuming the development and interest in spaceflight continues, we'll be seeing generation ships departing for the next solar system within the next 500 or so years (rough armchair prediction based on nothing at all). Of course, we have some massive problems to solve first, like biology, self-sustenance in deep space, cultural, financial, etc.

Anyway, my theory that we haven't seen other species yet is that space is vast and science fiction tech for light speed and beyond does not exist. If you have technology that can reach 1% of light speed, it'll take 10 million years to fly across just our galaxy. Humans evolved somewhere within that bracket. Even if the technology is there, you're seeing not just generations but entire species develop in the timescales of traveling the milky way.