We could put people on Alpha Centauri in 88 years with 50s technology like Project Orion. The really hard part is figuring out a way to make us use the technology we do have for things like that, instead of for bombing each other back to the stone age.
With that kind of propulsion politically available, I doubt finding workable combinations of mitigation strategies to interstellar medium hazards would be the showstopper. Especially not one to hold us back for time scales that oceans did. Getting humans interested in prioritizing projects like that, to me, is the real headscratcher.