This sounds a lot like Velikovsy's "Worlds In Collision". There was a freeze 13,000ya that probably had great bearing on the extinction but pairing it with a 40,000ya event is a pretty tough case to make.
The Last Glacial Maximum(LGM) was 18-23,000 years ago. One of the coldest periods during the Ice Age.
I don't think there were ever enough humans in ancient times to hunt any animal to extinction. 75,000 years ago, there were only 2-10,000 humans worldwide.