A study has been performed1 where more than 700 Genyornis eggshell fragments were dated. Through this means, it was determined that Genyornis declined and became extinct over a short period of time -- too short for it to be plausibly explained by climate change. The authors considered this to be a very good indication that the entire mass-extinction event in Australia was due to human activity, rather than climate change.
See also: History of Australia