It's believed that the Last Hero led the battle against the Others in the Battle for the Dawn.
The Battle for the Dawn ended with The Others being defeated and driven north by the first members of the Night's Watch.
It's not even a unanimity in the Maesters "community" that the Battle for the Dawn occurred at all. Most things related to the Others are obscure on a historical point of view, which makes impossible to determine with certainty when the Battle for the Dawn really happened, but the Maesters that believe that this battle happened, place it around 8,000 years before the beginning of the events in ASOIAF.
As the amount of documentation related to this time is scarce (and maybe nonexistent), it's hard to tell what was the exact conditions of the army that fought The Others.
Remember that before the Battle, the Long Night had lasted for many years (maybe more than a century), which definitely would have a huge negative impact on supply lines for the army.
And the further they marched north to drive The Others back to the Land of Always Winter, the harder it would become for the supply lines to reach the army.
The Battle for the Dawn could be seen as a somewhat desperate move after the First Men and The Children of the Forest found out what was the Others weakness.
They needed to battle them as fast as they could as more years of the Long Night would mean more years of famine, death and a smaller chance to win the war against the Others.
Below it's more an opinion based on the little knowledge we have about the age that embraces the Long Night, the Battle for the Dawn and the overall lore regarding the Others.
Another reason that would make the army of Men and the Children of the Forest
think twice before going full genocidal on the Others is: The Land of Always Winter was likely uncharted territory for them.
They didn't know what they would find there, probably, the only thing they knew by the time was that it was the Others "birthplace" and that it was a region colder than any place in the world.
Entering an uncharted region with such bad reputation and dwindling supply lines would be, to say the least, a dumb move.
The Others were pretty much defeated and forced to retreat, therefore it's wiser to march back to the safety of the south, gather your army, give your men some rest, and then start to prepare for the event of a second wave of attacks from the Others.