You can add a little fish food if you’re worried about starving the bacteria, but really, microorganisms can live pretty well off their dead brethren.
ETA: It is super important to test for ammonia, nitrite, and nitrate at least once a day if you add fish food and live fish to a new tank, even when using established filter media. It doesn’t take much fish food to crank the ammonia up to a point where it’s hard to get it back under control.
Cultivating live food for your fish friends is a great idea! Research, trial, and error are going to be really important in the process, so it’s better to do it in a separate tank to keep your fish safe. We don’t have the ability to bring an entire complex ecosystem into our homes and put it in a glass box; the best we can do is mimic one as best as possible. This means that an experimental tank won’t have as many of the same “redundancies” nature does when nutrient, light, or oxygen/dissolved gases get out of balance, and population crashes can happen a lot more easily. (Even if it’s just the food creatures that die off, the decaying matter can cause problems like ammonia burns for your fish.) Rather than trying to establish a sustainable colony of food animals in your fish tank, starting a tank with food animals and slowly adding fish to it will give you a much clearer picture of how large a population they can sustain.
Some tips to help you build as robust a system as you can:
This sounds like a really cool project. If you decide to do it, I hope you’ll post updates!