After you escape the Caged Suburbs, open the map and zoom out so you can see the map grid numbers and letters. You will want to head to grid L38 and/or O34. These both have a farm with a few patches of soil ready to grow plants (you can make more a bit later with a Hoe + Plant Matter). You will need to also invent the Seed Bag tool in order to plant seeds.
Once you have the Seed Bag, equip it and press
to select seeds and press
to plant on the tilled soil. Be aware, this consumes the veggies you have stored and each one takes a different amount. For example, you must have 1 carrot to plant 1 carrot seed, but you must have 3 wheat to plant 1 wheat seed. Onions and Wheat took me the longest to find, so just keep searching kitchens in the various buildings.