Could the Clues to Ancient Alien Civilizations Be Hiding in a Bucket of Moon Dust?

Most of our experience with the Search for Extraterrestrial Intelligence (SETI) has been focused on capturing radio signals that alien species have sent out, whether intentionally or unintentionally. That creates a huge synchronicity problem - what if there arent any alien civilizations broadcasting radio signals now, but there were a billion years ago? The Milky Way is around 13 billion years old - hoping that we exist at the same time as an alien civilization that happens to be actively messag...