The Stone Age may deserve a different name, at least for Neanderthals. A review of archaeological evidence argues that wood was probably at least as important as stone for making tools in Neanderthal Europe. The problem is that wood rarely survives in the archaeological record, so its role is easy to overlook.
Where wooden artefacts have been found, they show skilled workmanship. The review points to examples such as spears and other implements that would have required careful shaping. These finds, though rare, suggest Neanderthals had a substantial woodworking tradition.
The source article does not present competing views in detail, but it does note that the scarcity of wooden remains makes direct evidence thin. The conclusion rests on the idea that absence of evidence is not evidence of absence: just because few wooden tools have been found does not mean they were uncommon.