How to Get Modern Axe Instantly
When you spawn on the island just walk to the camp marked on the map, there are many points to orientate yourself. Like the cave or the special looking little lake. If you walk to this place, there is a camp with 3 tents, one corpse has an ax stuck in it.
You can use it to chop down trees much faster right from the start.
Just a little walk through the woods
If you walk to the marked spot, you will find a camp with a corpse with the axe stuck in it.