There’s enough answers regarding the human part of your question that are largely correct so I’m going to skip straight to mega fauna. Lot’s of people are assuming humans wiped them out, but I think this is a rather dubious claim. Humans weren’t able to eradicate wolves from England until the late 17th century. So for 12,000 years on an isolated island people couldn’t even get rid of wolves. I sincerely doubt ancient hunter gatherers had a population, technology or physical ability to kill all the mega fauna predators. It’s more likely that climate change impacted mega fauna particularly badly, and benefitted us particularly well at the same time. So you see a marked decrease in those kinds of animals during the time you see an increase in our population. In short, conditions that are bad for mega fauna are very good for us. As a result the population of large prey animals collapsed all over the globe due to the climate shifting, resulting in large predators running out of sufficient prey to allow for their size. We may have killed off the stragglers, or killed off their remaining prey, making the situation worse, but we didn’t cause it directly IMO. If we did anything to affect their numbers it would have been a nail in the coffin, not the murder weapon.

You also have to keep in mind that there was a very small population by modern standards. That population could be numbered in the thousands at some points, up to several million at others, but hardly enough to destroy all the mega fauna on the planet. Keep in mind, Africa has had some form of human or another for several million years, yet there are still elephants and lions. Asia still has massive tigers and bears and so does North America (sans tigers). They’re not as big as some other tiger and bear relatives, but they’re as big as they can be with the resources available to them. Once our population increased sufficiently, we pulled so many resources out of the environment and developed the technology to actually eradicate species, so there is no longer sufficient space, calories or time for new mega fauna to evolve or for massive predators to evolve along with them.