There was an episode of “Star Trek”, something like “The World Is Hollow And I Have Touched The Sky”, in which an entire population is traveling to a new destination, but unknown to them.
It was one of the better episodes but basically the idea is too far fetched.
They recycled the idea in Next Generation.
It will happen. Once a big chunk of humanity is living that way every day within rocks orbiting the sun, pushing one of those towards a nearby star system will be relatively simple.