The milky way galaxy alone is 100,000 light years across. So even if you had a way to travel at the speed of light, it would take 100,000 years to travel from one side of one relatively small galaxy to the other.
,...and there's billions of galaxies out there,..each of them containing 100's of billions of stars.
And each solar system inside each galaxy is on its own time line. Any system which might have eventually developed intelligent life, that intelligent life only existed there (or will exist at some point in the future) for an infinitesimal blink of an eye during the 14 billion years since the origin of the universe.
So it is not just a matter of searching out the point in space where such a species might exist, but also being there at the proper point in time.
