I'm not sure quite what you mean - life like Earth's can't occur until conditions are suitable to support life like Earth's (the micro-anthropic principleThe LCDM cosmology model still violates the Copernicus principle by suggesting that we're living in a privileged position with respect to time.
Most of the rest of the life of the universe is projected to be populated with black holes evaporating until the indefinite heat death period. Compared to that timescale, there's a relatively small window of opportunity early in the life of the universe that is suitable for the emergence of complexity - it's no surprise that we find ourselves in that window.
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