Did climate change wipe out the mega-fauna

Around the time of the transition ~12,000 years ago between a world with continental glaciers as much as 3km deep, extending, in North America to below the USA-Canadian border, and our present more benign climate, mega-fauna disappeared from a number of Islands  and continents.  So was this due to the change in the climate as we left, what is popularly called and Ice Age to our present warmer climate.  First we have to establish some terms and a little background.

Over the past 2.75m (million) years, the world has gone through about 40 cycles of Contental glaciers and warmer periods like now.  During the first half of this period, the cycles were about 41k (thousand) years while over the past half of this two and three quarter million year period, cycles have been about 100k years.  The exact timelines are hard to establish because each period when kilometer thick glaciers moved across the landscape, they wiped out the record of previous glacial an interglacial periodsl  

All is not lost, though.  And Ice itself is one path to documenting past fluctuations.  The Antarctic has been glaciated for at least 34m years and the ice is built up in layers which are much like tree rings.  Generally (not always) one layer is laid down per year.  And this record goes back pretty reliably for 800k (thousand) years.  In addition there are ocean bottom sediments and a peculiar meteor crater in Northern Siberia called El'Gy'Gytgyn that has a sediment record over 3.6m years.  

Something interesting that has been observed from these records is that for the first half of this 2.75m year period of alterations between icy and less icy times, the cycle length has been about 41k years while for the second half of this period, the cycle is closer to 100k years.  Incidentally, the previous warm period goes by various names but the one that many 'westerners' use is the Eemian interglacial period.  

In the popular literature and even some scientists call the most recent glaciated period an Ice Age.  I have no objection to this term (not much!!!) but if we use it to describe the recent glaciated period then we have to find a new name for the 2.75m year period during which we have had all those alternations between warm and cold periods.  

So for the rest of this diatribe, I am going to call the last 2.75m years an Ice Age and will call glaciated periods Glacial Periods and the warmer interglacial periods, Interglacial Periods.  At present we are in the so called Holocene Interglacial Period and as mentioned the previous one was the Eemian Interglacial period.

Now we come to two problems if we want to hypothesize that the transition from the recent Glaciated period to the present Holocene Interglacial period caused the demise of the immensely varied mega-fauna of the Americas.  

I think everyone would agree that, based on our present knowledge of how long it takes to create a new species, that all this megafauna didn't evolve over the past 100k years.  In other words, the ancestors of the elephant types, Camel types, Giand sloths, Giant beavers, Equinine species and so forth existed at the start of the 2.75m Ice age that we are still in and undoubtedly evolved special adaptations to glaciation over the 2.75m year ice age.

The critical point is that they didn't go extinct, either during the slide from a warm period into a cold period or vice versa.  And there were at least 40 such transitions.

The second problem is the evidence from other continents.  The incredibly varied population of mega-Marsupials and Monotremes in Australia went extinct about  50k years ago, just as man arrived in Australia.  The amazingly varied mega-fauna of the Americas disappeared around 12k years ago, just as the first people spread through the Americas and the mega fauna, consisting of giant ground living birds, plus a giant eagle and many species of 'dickie birds' disappeared 700 years ago just as the first people arrived in New Zealand.

The only conclusion that seems reasonable to me is that in every case, the first people into a new land were responsible for the demise of what they found there.

This leaves a contrary problem.  How did the mega-fauna of Africa survive until Europeans arrived in the continent were man evolve.  The only explanation I can think of is that the animals evolved a fear of man as man became more and more able to kill them and to kill them at a distance (spears, then throwing sticks and then bows and arrows.  They would have learned that when the strange two legged animals were around, they kept getting hit by heavy and pointy objects.