The consensus (1, 2) is that the reason most continents have relatively few large animals compared to Africa is that humans, even stone age humans, were able to drive them to extinction. African animals survived to some extent because they had time to adapt to us before he had decent weapons.
What could prevent an expanding human civilization from driving to extinction the megafauna in a newly-settled area?
For the scenario I have in mind, humans have early-Renaissance technology: iron and steel, some gunpowder arms, sophisticated governments with the ability to finance exploration and conquest in remote areas. Magic also exists, but I'd prefer not to handwave with "a wizard did it."
One simple answer is that these humans simply value large animals more than... any people historical ever have. Yet even if there's some interest in and understanding of ecology, it's hard to see how that could prevent hunters from knocking out the largest (and presumably slowest-breeding) animals like Elasmotherium.
Note that a few large animals did survive humans' arrival - bison, kangaroos, llamas. I'm looking for reasons why an area may plausibly retain a substantial quantity of large animals despite, say, a hundred years of very low density settlement (trappers, prospectors, a few trading towns) and another century or so of low density farming and hunting.