Food is tough but doable. Here's what you're looking at:
- Look for roadkill. Not to eat, but harvesting them yields valuable bones for shivs (meat!) and glue. Always, always worth it to smash them when you find them (on concrete roads)
- Do a 'treasure hunt' mission for the trader. The chest has almost always contained food/water/rations for me. You can take potshots at animals along the way if you see them.
- If you see potatoes, grab some. You can bake them for food without a pot or grill. Do not eat them raw!
- Grab eggs, boil them if you find a pot.
- Focus your scavenging efforts on residential houses and only worry about the kitchens and bathrooms for bottles, pots, and if you're lucky, a grill. You'll usually find morsels like canned peas and dogfood
- If a rabbit stands still, kill it and give its still-warm skin to a child who needs socks. If you see ANY animal, kill it regardless of what you're doing.
- Giant poltergeist pigs are hell to kill, but are fully edible and worth it if you can take one down.
- If you have meat, save it for bacon & eggs. It's the most efficient food in the early game.
- If you're finding yourself VERY hard up, take the Slow Metabolism perk and eat eggs raw... I've had to do this a few times.
- If you start in the snow, or desert, kill yourself now. There's no food in the snow biomes, and yucca plants aren't enough to subsist on. The only animal I've seen spawn in the burnt biomes now are rabbits. You used to see deer there..

You need forests or bust in this game now.
- I see a lot of town POI's have farm plots or even gardens where you can find corn, potatoes, and even blueberries. I think there's one nearby in my game that has a few yucca plants. If you're going to explore and scavenge, keep an eye out and bookmark them for later.
That said, animal spawns appear to be much less common. I used to be able to take a day hunting and at least bag a couple of deer, but now, I'm lucky I find 1-2 strays a week.
If you can find a working stiffs, or if you work for the trader for a bit, you can sometimes score a hoe. I do NOT advise starting a farm between day 5-7, simply because you need to focus on horde night. It's usually a good 'morning after' activity.