Where's that cartoon of "...then a miracle happens." when you need it?
If this conjecture was even possible, then EVERY star system in the universe would have a Civilization that has arisen and is trying to contact one another.
(They've ALL had the same amount of TIME that we have had.)
Obviously possible because we are living it. The chances of it happening to others? It has to be small because we have been looking for radio signals for decades without finding any signs .