Did humans have neanderthal ancestors in the Star Wars galaxy. Were cavemen ever mentioned in canon, or even seen?
Not really, since the origins of humans are way too far back to be known (even the home planet is an unproven hypothesis in-universe).
The earliest origin story of humans in TGFFA are Zhell, of which nothing is known as far as pre-history:
The Zhell were a people indigenous to Coruscant and the possible ancestors of the Human inhabitants of the world. They consisted of thirteen nations known as the Battalions of Zhell.
... Since Coruscant was considered by some to be the home world of Humanity, several historians hypothesized that the Zhell species may have been the ancestors of the Human race in the galaxy.
Also, from Human Origins on Wookieepedia:
Coruscant's ground had been several kilometers below its inhabitants' feet for millennia, with the lowest depths of its planet-wide city dating back to 100,000 BBY. Thus, it was impossible to carry out the historical study and archaeological research on the planet's prehistory necessary to prove or to disprove that theory.
In addition, Coruscant's natural climate was said to be too cold to support Human life, a claim difficult to be reconciled with the theory that it was the original Human homeworld. Tarnese Bleyd believed that the ancestors of Humans favored trees and high ground based upon his observations of human hunting behavior.
Sources: Star Wars 84: Seoul Searching, The New Essential Chronology, MedStar I: Battle Surgeons, The Essential Guide to Planets and Moons.
The canceled book Alien Exodus established that the humans in the Star Wars galaxy were descended from humans from Earth in the 25th century that were enslaved by the Rodians. This is the closest link to Neanderthals in Star Wars, although since the book was canceled, it is non-canon.