There are two ways to preserve megafauna as seen in our world’s history, and the two case studies will serve as names for the models.
The Madagascar Scenario
Elephant Birds were the largest avians to ever tread the earth since the K-T extinction 65 million years ago, and they survived well into the Middle Ages. This is because human beings did not reach Madagascar until this time, so the Elephant Birds were spared human depredations. So one easy way to retain megafauna is to simply have significant regions that are geographically isolated from humans as to prevent any interaction.
The Afro-Asiatic Scenario
Mammoths and Mastodons are dead, yet elephants remain in Africa and Asia. While the exact reason as to why elephants and rhinos survived humanity while their wooly cousins in Europe and North Asia didn’t, one theory is that they were wise to the ways of human hunters.
Take the zebra and the horse as smaller examples. Horses were driven to extinction in North America by Paleo-Indians, and Wild horses very nearly suffered the same fate in Eurasia (their domestic cousins don’t count). But Zebras are still abundant to the tune of hundreds of thousands if not millions.
This is because Zebras take absolutely no shit from humans. Just try approaching one and you’ll learn really quick why they’ve never been domesticated. Zebras are very quick to run, inherently distrustful of humans and aggressive in defense.
To have your charismatic megafauna exist in proximity to humans, make them wary beasts who are quick to run or fight humans. There is a reason why the elephant bird is extinct and the tiger is not.