In this case no one is even talking about FTL travel. Just fast. Around 12% the speed of light is what we’re currently technologically capable of and that’s damn fast.
One of the interesting forward shielding ideas I’ve seen is pushing a large cloud of tiny aerogel spheres ahead of the craft to snag those little particles that would kill a craft. The big ones would be easy enough to steer around.
We get the impression of asteroid fields being these rocky minefields that you would have to carefully thread your way through. The reality is that the average distance between asteroids in our asteroid belt is more than a million miles.
/johnny