You could make an argument for Carthage being a genocide but I'm not sure the Romans ever went to war with the extent of exterminating an entire people.
I'm not sure how much more explicitly you could be calling for the absolute extermination of an enemy than
Carthago delenda est, or in its wordier form,
Ceterum autem censeo Carthaginem esse delendam. Other shit Cato often said was very explicit he meant the actual death of everyone in the city.
The Mongols were also famous for systematic extermination. See also: Assyrians, Zulus, Huns, Turks-- Even the Athenians got in on the action during the Punic War, slaughtering the populations of disloyal allied states.
Genghis Khan was actually pretty progressive as murderous, genocidal warlords went. He was actually a huge fan of religious tolerance and offered his potential tributaries (or genocide victims if they picked that path) a pretty nice deal for the time. Surrender to us, you get to keep your religion. Don't? You all die. Plus if you join us nobody else gets to attack you, or we'll fuck them up, because you're
our bitch.
This was a great strategy because it not only presented the threat of immediate death, but separated the populace (including the military) of the country from its rulers, who were well accustomed to expecting religion to motivate their population to resist invasion. With Genghis, though, who was obviously about to kick your ass entirely, you had the choice of a pretty prosperous life in a successful empire, and just getting raped and murdered.
This is really the Roman model too. Look at any successful model of human society where you actually know their names even if you are not a gigantic nerd who actually read Decline and Fall of the Roman Empire by Gibbon and know how much shit the Romans actually wiped out.
Is it any wonder he succeeded? Genghis was maybe the first multi-culti. Consider his success. Wonder why.
Also just contemplate this, cultures are dying out on a daily basis. Look up the lists of the last native speakers of some specific language. You will be amazed. Some last living speaker of a language dies every week or so. Some 100+ year old motherfucker who grew up speaking some language dies as its last speaking member. We are all dying. Every day.