Can't start the "go to war with another empire" mission
You will be unable to do this mission if there aren't any empires you don't have an alliance with near your home world. If you've eradicated all nearby empires, but still have an empty system nearby, dropping some life forms and a monolith there will create a suitable target. If there aren't any unoccupied system, you can always destroy your colonies in a system and do the above.