Hard to say for sure in the case of warm blooded creatures. Insects have a direct relation to O2 levels and size. But gigantic growth in others tends to be an adaptive evolution to stable conditions to essentially brute force their particular niche in a ecology. O2 does factor into it as well. A human in some parts of history would have issues because the general o2 levels fell so low that it would be uncomfortable to toxic. The post permian extinction period is an amazing example of this. But it needs to be a swing of o2 more than double digits to have a noticeable effect on fauna in most cases. In the case of the gigantic growth we saw during the Pleistocene it was more of a case of isolation for this particular bird. They became the apex because things were stable for so long that they could do it without competition. When the Panama bridge formed towards the end of the period, and the north american predators began to compete with them, terror birds largely died off because they couldn't compete with the more generalized hunters. Then when the ice age began to end and the world conditions began to warm, it was the end of the road for most of these gigantic creatures because the stable conditions they relied on changed and they weren't prepared to adapt. We've actually seen this happen a LOT of times that didn't include a cataclysmic extinction.