Only if we figure out how to get off this one solitary rock and expand beyond the solar system. The sun (Sol) will continue to go through its natural processes which will see it expand larger than the Earth's orbit. That will be the end of physical Earth, but life as we know it will have ended before then.

So, I'm not sure who the "we" will be that will have less than 14 billion years.

Well, I, for one, don't plan on being there when it happens!