Our entire perspective on existence is based on where we popped up on the cosmological timeline. If we'd come along earlier, we may not have been able to perceive the expansion of the universe, and the apparent disconnect between the hard limit of the speed of light, and the size of the universe. If we'd come along later, we may have figured that we were completely alone in a static sphere, with no observable matter outside our galaxy.
I also find it fascinating that if we had come along a few thousand years earlier or later, our entire history would have been completely different. How effective would we have been as travelers if the north start didn't exist for us as guidepost in the northern hemisphere? So much of our existence is based on lucky chance.
“You know, the most amazing thing happened to me tonight. I was coming here, on the way to the lecture, and I came in through the parking lot. And you won’t believe what happened. I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!”
What's really spooky is thinking about the things which we would have been able to observe if we had been around much earlier. Perhaps seeming constants have changed over the history of the universe, or other universes which drifted away from us along now-imperceptible dimensions. (I'm guessing you saw the same Brian Greene TED talk I did.)
Lawrence Krauss's longer talk in Toronto†[1] has a better explanation of the "privileged time" idea (and doesn't invoke string theory except to poke a bit of fun at it).
† Krauss has given more-or-less the same talk elsewhere, but the version recorded by TVO (the Ontario provincial public broadcaster) is probably the best recording. [Edit: I misremembered the location of the talk. Most of the physics talks on Big Ideas are from the Perimeter Institute; Krauss's wasn't.]
I also find it fascinating that if we had come along a few thousand years earlier or later, our entire history would have been completely different. How effective would we have been as travelers if the north start didn't exist for us as guidepost in the northern hemisphere? So much of our existence is based on lucky chance.