We may be in a simulation, but your odds of being alive to see this (conditioned on being born as a human at some point) aren't that low. Around 7% of all humans ever born are alive today!
Given that we only hit the first billion people in 1804 and the second billion in 1927 it's not all that shocking.
But this is also just the non-intuitiveness of exponential growth which has only now tapering off.
You could go back to Lucy and add only a few million. Compared to the billions at this specific instant, it just doesn't make a difference.