Note that a journey to a star a 100 light years away where you accelerate and decelerate with a constant 1 g for each half of the journey only takes 9 years of subjective time for the traveller (hence the twin paradox). To Proxima Centauri (4.24 ly) the gain isn’t as dramatic, it would take 3.5 years of subjective time.

Of course, we aren’t anywhere near having the technology for that, and there may not be any suitable planets in that vicinity, but it also doesn’t seem completely impossible.