Sorry. I wondered out loud. However I do know some things: alligators were predators of our ancestors millions of years ago. I wonder if that remained so up until recently.
The current largest predators are a mix of saltwater crocodiles and nile crocodiles. And they have existed for a long time, so they certainly were in the past too.
(obviously the biggest human killer is mosquito but that is through disease and not a direct result of predtion)
Ok first want to thank you for good word usage.....no sarcasm. But you have to consider disease. Because if our ancestors killed something you have to think how long it was before they knew how to cook something. So I am betting more on disease or untreated cuts or injuries that was as you put it the major predator.