A first Contact like in Contact, which provides a solution beyond our known physic laws, is the only way this could possible.
With Lightspeed alone, we will never reach anything outside the Sol System.
The Center of our own Galaxy is 150k Lightyears away. The next Galaxy, Andromeda, which is basicly in our backyard is 3 million Lightyears away.
Not even with with a Lightspeed fast Generationship we would reach anything.