You don't notice the tremendous speed at which you are moving because all the things around you are moving with you. An observer standing outside your galaxy would see that you are moving at a speed of over 250 million mph.
The marble stopped moving - and the rest of the universe kept moving.
That marble "travelled" (relatively-speaking) away so fast you couldn't see it leave.
The capability of Interstellar travel is required for continued survivability (because Earth is doomed).
Propulsion using a fuel source carried onboard probably isn't viable.