Achieving faster than light travel from the perspective of the crew may not require actually moving faster than light. It just requires some out of the box thinking.

Suppose your crew consists of brain uploads. Your spaceship is basically just a computer that emulates their consciousness, gives them virtual bodies, a pleasant virtual environment and so on.

Because both the speed at which cognition is emulated and the passage of time itself within the simulation are dependent on the clockspeed of the machine they’re running on, you could throttle it down as close to zero as you like.

From the perspective of the emulated crew members, time outside of their ship would be passing extremely quickly. You could even just halt processing at the point of departure, then resume at the destination. From the crew’s perspective, transit would have been instantaneous.

The ship would be equipped with generalized fabrication facilities which, upon reaching the destination, could build them artificial or even biological bodies out of local resources. A store of genetic information and artificial wombs could be used to populate the planet with a sufficiently diverse breeding pool of human colonists.

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