According to wiki [1]:

> At a constant acceleration of 1 g, a rocket could travel the diameter of our galaxy in about 12 years ship time, and about 113,000 years planetary time. If the last half of the trip involves deceleration at 1 g, the trip would take about 24 years. If the trip is merely to the nearest star, with deceleration the last half of the way, it would take 3.6 years.

24 years is one generation of humans. And 113,000 years is still less than 600 million years. Speed of light is not a problem. Making that ship self-sustainable and even being able to accelerate to 0.999 c might be.

[1] https://en.wikipedia.org/wiki/Space_travel_using_constant_ac...