If we can figure out how to solve our political issues and become a eusocial species, we may be able to build some generational starships. In 4.5 billion years we could potentially colonize many of the planets in the habitable zone of stars in the Milky Way.

Sure, it could take millions of years to cross the galaxy, but we could grow exponentially (like lily pads crossing a pond), at least until other limiting factors kick in.