We Called Out To the Stars, and Nothing Answered
I hate to be that guy who rains on creativity, but there is no possible way that humanity could have figured out that the galaxy was devoid of intelligent life in a week. Even if they could instantly travel to any star in the Milky Way, there are roughly 200-400 billion of them. If the drive you speak of takes 24 hours to arrive at any location, it would take anywhere between 28,571,428,571-57,142,857,143 ships to all leave at the same time. This is not accounting the time it would take to actually explore any of the star's planetary systems either.