Poached eggs are still only 5 hp, and killing birds is very unsafe at the start of the game. They do 18 damage! I haven't found any sunflowers at all?
Apples are the best you can get but are rare enough from trees that I must have chopped enough trees to get four stacks of wood and only collected 10 apples. I've got a bunch of potatoes but baking them doesn't give a regen effect so they don't restore enough HP to make recovering from combat viable. If there was ANY passive healing at all this wouldn't be as much of a problem since you could just afk in your house for a while to recover after dying or getting hit a few times...
I would try farming but I haven't found any gravel, and trying to explore caves to find it is risky because as mentioned you can't recover well from early combat.