The oldest comb that I have reference and photography is dated to the 1rst Century BCE in the Dead Sea region, after that they begin popping up all over the world, Ireland and Scandinavia had a booming trade of making and selling bone, antler and horn combs, maybe wood too
Here are pictures of combs that I have amassed from all over Europe, on the internet and from friends, I've lost track of their sources.
Most of these are made from antler but there are some wood ones mixed in.
Looking at the historical ones we find clues to technique and construction methods, there are also clues to what tools were used. Put on your investigator hat and take a close look at all of them then move on to the next step