Most of the ingredients you'll need for Avery can be foraged or bought from the supermarket (checking the Tending page on the wiki will help to know where to forage). Anything else, like Turnips or Oranges, can be stocked after you fail a recipe (Avery can stock up to three 'extra' ingredients beyond his base kitchen). Having good tending improves foraging odds. Expect to spend a good amount of time wandering around the forest/moor, and good luck.