As far as I've seen all the cultures have the bare basics, although they're rarer in the more remote cultures, so you should be able to get an axe in any culture provided you visit a sufficient number of villages.
If, for whatever reason, you find yourself unable to get hold of an axe you can make a stone axe (which is a really poor axe, but it allows you to do some things, although not all, e.g. not a paddle to get you off an island...). The next step would be to either kill a Njerp who has an axe or to mount an expedition to richer areas, which definitely is required if you're looking for masterworks everything. Obviously, an expedition requires something to trade with, which usually means hides.
You can build your homestead with any axe that's not a stone axe, but it's quite a lot slower with unsuitable types.