>>12728216Probably sending a targeted friendly message of greetings to let them know we are out here and then waiting a gorillion years until it gets there and for them to reply back.
In the meantime try to study their star system with very little data and lots of speculation.
First contact of this type (the most likely) would probably be incredibly boring and underwhelming. It would be decades if not hundreds of years before we glean anything meaningful from it.
And in the end perhaps we discover that what we thought was a biosignature was actually a necrosignature and the civilization responsible for it has long gone extinct.