Animals become easier to hunt during mating season.
As for births, assuming the ancients didn’t have modern age restrictions on harvesting the young, that is also a time when the mothers and their offspring are more vulnerable.
Animals become easier to hunt during mating season.
—
If you want to preserve the local game resource, you do not hunt them during at season, absent a government agency setting rules. Also remember during that time humans were few and animals were plentiful and very dangerous to hunt.