If you're ok with using mods (and assuming you're on PC), there is a mod that not only overhauls the cooking in the game and adds a bunch of real ingredients like eggs, cheese, flour, sugar, milk, etc, and let you buy said items to cook, but they've also created a grocery store to go with the mod.
SrslySims Complete Cooking Overhaul |
Greenfield Grocery Store lotThe mod also allows you to go to a rabbit hole grocery store to quickly buy fresh ingredients (all fruits, veggies, herbs, flowers, fish, spices, etc) when you need to.