If you aren't playing innawoods I would recommend maybe finding nearby houses as there is a lot of food that is going to spoil anyway. The zombies aren't too bad in the early game and you could always kite them piecemeal or night raid without too much trouble once you get into it.

Looking through the all the underbrush can get you wild herbs which is quite versatile ingredient.

If you are near water you could and find and kill water bugs but needs to eaten sparely as emergency ration, but don't rely on it as I have learnt that too much toxins in the mutant meat ends up having your character getting spasms which is not fun, also bug killing bonus with stockpiling chitin and sinews.

Chickens are a great source too for meat and eggs but should really be keep in a safe secure location and needs regular culling to keep the numbers and frame rate reasonable.

I guess the advice is very situational but I hope it was helpful