I apologize for the weird question, but based on a Google search it looks like this topic hasn't been discussed before. I'm hoping that enough information about population biology is stored in the fossil record to answer this question.
Humans have wiped out a lot of animals in a very short time, but I realized that mammals might be doing very well.
First off, humans are mammals, and there are 7.6 billion of us. That's quite a lot. I don't believe any other animal species of our body size has such a large population.
Second, humans have pets. A lot of them. And they're almost all mammals. Everywhere we go we take our cats and dogs with us. Many of them become feral and multiply prolifically.
Third, our livestock. With the growth of human civilization came the growth of meat consumption, which, naturally, meant a lot more cattle. I think I read somewhere that cattle are contributing more to global warming than cars, through burping.
Lastly, and probably most importantly: rodents. Cats chased us everywhere because rats chased us everywhere. They thrived on the grain we grew and their population exploded to the point that they became a global pest, and possibly humanity's greatest enemy.
So, my hypothesis is that there are more mammals now than ever before in the history of life. Not in terms of species diversity, but in terms of headcount. If this is true, it would be remarkable, since the rest of the Animal Kingdom is currently suffering through a mass extinction.