What I mean is that you are injecting assumptions about how you came to be a conscious entity on Earth in whatever year your mother conceived you, as opposed to any other place or time in the history of the universe.

Maybe it's true that for every sentient being you assign equal probability and then it would look very odd indeed that you ended up in a early stage civilization in an old, empty universe.

Or, maybe coherent worlds count as a single state, therefore greater probability mass is given to later civilizations which exist in a good deal many more Everett branches.

Or more likely it is something completely different. The very idea that I was 'born into' a sentient being chosen at random stinks of Cartesian dualism when I really look at it. It seems very unlikely to me that the underlying mechanism of the universe is describable at that scale.