As Dyet1300 suggested, finish getting 3 stars on every level before grinding this out.
Level: 1-1
Method: Sign in a second player, even if boosting by yourself, to speed up the chopping speed. Grab wood and go to the right chopping board. Then immediately turn right and throw on to the bottom right campfire. Then grab more wood and repeat. Going in this tight circle can get you 1 piece of wood every 5 seconds. There’s no need to finish the level either, as this will unlock automatically once you’ve thrown your 300th piece of wood on to the fire.