That's only one generation that would need to be raised on a ship

If we managed to build the ship and if we managed to get it to same speed as our fastest space probe, it would take around 35000 years.

It might as well be a billion. Humans in our current form can't survive interstellar travel. We would need a far more durable substrate.

At 99% the speed of light it will take the traveler less than three years, while 20 years passes on earth. If they then turn around they will return to earth, they will arrive aged 6 years while 40 years have passed on earth. You can come back younger than your children.

Which then makes for an interesting moral or ethical dilemma: is it ok to embark on such a mission after having children, knowing that they will live half a lifetime without you and, assuming you left before the age of 34, will be older than you when you get back.

Generational migration can be done.