I'm note sure that is the case. The universe is approximately 14 billion years old and the heavier elements were formed in supernovae. So for planets and life to arise, it had to be in the second or third stellar generations. Intelligence also took 4 billion years to come to fruition on this planet, why not others. We all may be emerging about the same time. Some sooner others later, but the history of the human race is such a tiny time compared to the time life has been on this planet.
I would wager my life savings that we DON'T have a billion years, or even tens of millions of years, to work with. If a large comet or asteroid doesn't cause a mass extinction before then, an all-out war almost certainly will.