It could be that climate change precipitated both human technological evolution, which in turn led to the massive expansion of the human range, and the mass-ext

It could be that climate change precipitated both human technological evolution, which in turn led to the massive expansion of the human range, and the mass-extinction of mega fauna. Climate being responsible for both would explain why the extinction was global in scale and coinciding with the spread of humans. This is not to say that your theory is wrong. Just that this is a potential alternate explanation.