To explain, it wasn't that long ago that humans walked alongside mammoths and smilodons. Is there any sort of evidence that humans from early civilization had any knowledge of these animals, through oral tradition or whatever?
I know of no efforts to link any recorded oral traditions to Pleistocene animals of any sort. Information about these animals come from paleontological discoveries including frozen remains and from rock art, the only human records known to exist about these animals.
I would be extremely skeptical of any attempt to "see" references to ancient, extinct animals in recorded oral traditions.