I’ve always wondered how the cavemen could be reconciled on a time scale with Biblical teachings of Adam & Eve being the origination of humans?
Use the same definition of "human".
As for Neanderthals, Creationist models vary. One idea is that modern day Europeans and people in the Levant and Central Asia (the places where Neanderthals used to live) are the descendants of Neanderthals.
Another is that they could have been people who actually obeyed the command to spread out after the Flood, and sort of became a subspecies of humans while the rest of humanity loitered in Mesopotamia, and after Babel, some of those Mesopotamians--the ancestors of modern mankind--wiped out the Neanderthals.
A rarer view is that Neanderthals were humans living in the antediluvian world; this hypothesis is chiefly for other advanced hominids such as Homo erectus and Homo habilis and similar homo species (as in Latin nomenclature)--less advanced homo species were probably just types of ape that have since gone extinct (and humans aren't apes).