It's theoretically potentially possible to travel in a way that is effectively the same as if you were travelling faster than the speed of light. Maybe. Perhaps. The maths works. Or so I've read, because it's way over my head. But I'm talking about serious work by theoretical physicists, not crackpots. Miguel Alcubierre (sp?) was the first one to write a paper on it, but there have been others since. Essentially, you compress spacetime ahead of the ship. A "warp bubble". The ship doesn't move faster than the speed of light within the universe, so the speed limit isn't being broken. Nobody has any idea how that could be done, but apparently the maths works so it's potentially theoretically possible.
There are a few caveats and they're rather big ones. The original maths required negative mass/energy, which isn't a thing. The latest maths does make it possible with positive mass/energy, but the energy requirements are ludicrous. The equivalent of accelerating an object with the mass of a passenger plane (pretty small for a spaceship) to the equivalent of the speed of light would require energy equivalent to transforming about 20% of the entire mass of the sun into energy at perfect efficiency. That's also not a thing. That's far more energy than the entire energy output of the sun over its entire main sequence of billions of years. And that's just one small ship warping once and only to the equivalent of the speed of light. Higher speeds and/or more mass would require even more energy.
But it's not definitely absolutely impossible. Almost, but not quite.
Even if it is possible and some other people have dicovered a way to do it in a practical way, even if their ships can travel at an equivalent of many times c, I think the "just too damn far apart" thing would still apply. Even if the travel time was feasible, how would they even know we were here? The signals we've been leaking into space in all directions aren't that obvious and aren't feasibly detectable very far away on the scale of the universe.
Also, why are you of the opinion that there absolutely has to be alien life out there? Presumably alien life of at least our level of intelligence and aptitude for tool use, since you're talking in the context of space travel. I'm of the opinion that we absolutely don't know.