sigh... the science is weak in the OP.
The universe is between 13-15 billion years old. Exact figures are meaningless, as time is relative. To a beam of light, no time at all has passed since the Big Bang.
The earth should continue for about another 4 billion years. Humanity has much less time though, even without any human influence taken into consideration.
It took a real "perfect storm" of circumstances and events for evolution to bring about the modern human species, and our hold here is quite precarious. Even a slight deviation is the sun's energy output or the earth's orbit or whatever could be disastrous. Still, due to the ridiculously infinitesamal space of time our entire lives occur in, and subsequently the relative rapidity of our evolutionary progress, the odds seems to indicate that we will have many thousands of years of safety in which to evolve beyond the confines of this little planet.