You'll want to read "The Eerie Silence" by SETI lead Paul Davies who's job is to think of this stuff. The book covers many many possibilities for how a civiliz

You'll want to read "The Eerie Silence" by SETI lead Paul Davies who's job is to think of this stuff. The book covers many many possibilities for how a civilization might try to communicate or get the word out from Von Neumann probes to leaving something in our DNA, which could easily last multiple millennia to monuments...etc etc. It also covers the search for life elsewhere like looking for reverse chirality DNA on Mars (basically there is no reason all DNA found on earth should curl one way and finding DNA that goes the other way strongly suggests it didn't come from us).