I'm satisfied that Neanderthal had the dexterity and eyesight necessary to do needles. At the same time they, like everybody else in the world, probably made their needles out of wood and bone, both highly perishable
Now, the tough one, find a paleolithic stainless steel needle.
That's your standard of proof?? Try doing a google search on "neanderthal needle"; what quickly turns up is any number of statements attesting to the fact that nobody has ever found one.