Tip: You do not need a Bronze axe to fell a Birch tree.
You can fell Beech trees with a stone axe and then learn the art of log rolling to damage a Birch enough until it falls and then do the same to break the Birch logs into usable fine wood.
This takes less than 20 minutes, which is a lot less than 30 hours o.O
The same technique can be applied to core wood later ;)