You do not need to own your home to grow your food. Some of the best gardens I've built are entirely in containers, designed so the whole thing can move house with you.
The rule is simple: nothing goes into the ground, nothing gets screwed into a wall you'd lose your deposit over. Grow bags, stacking pots, a railing planter that lifts off — these carry your garden to the next place intact.
Think of the pots as the investment, not the spot. Good containers and good soil mix are yours for years. The balcony is just where they live for now.