I don’t see why not. Think of our progress so far. We have gone from walking, to horse transportation, to automobiles, to Flying, to space travel. I don’t see why not some time in the near future we develop the means to go faster still.
Will it be safe for humans is another thing. Remember before space flight were the flying tests going faster then the speed of sound. Everybody was afraid of what would happen to pilots then. But it was proven nothing happens. Then space flight happened and we were all afraid of what happens if you go into space. Turns out everything could be overcome to a certain degree here too.
I think first what will happen is that we upgrade space engines from chemical to nuclear power. Maybe in 10-15 years. Which heats propellants up to such a degree that you can go a lot lot faster then just plain on chemical rockets. Then maybe in the near future 30-40 years we figure out how to use fusion reactors and we add that to space vehicles and go faster still. I see in far futures 50-60 years we finally tame anti-matter propulsion and fgo faster still. After that? Who knows. NASA has teams working on future possible propulsion technologies. But don’t expect them to come up with anything soon. They are thinking way outside the box and if anything comes to fruition it could be 70-90 years away.
But remember technology moves fast. All my time tables could be drastically altered if some new technology is discovered that speeds things up. All I know is that right now we are using telescopes to infer planets existing around other stars. In the near future we may be able to actually take a picture of one. And what pushes people to get some where? News of a new world.