Hopefully not long at all if the bacteria are established.
You'll know when your tank is ready for fish when you can add 4ppm of ammonia to your tank and there be 0 ammonia and 0 nitrite twelve hours later, and you can keep doing this for a week. It's not only about being able to process it, it's how long it takes to do it.
ok silly question, but why would you add ammonia to a tank?
This is "fishless cycling" in action. You add a known concentration of ammonia to your tank and then test for when the ammonia processing and later nitrite processing bacteria have began to colonise your dechlorinated water.
You could add bits of fish food instead, but this method will take longer and is less precise in knowing how strong your bacteria colonies are.
Are you doing your cycle fish in, or fishless? Apologies, I just assumed.
fish in cycle and before you ask they are all doing great very healthy and showing no signs of stress lol
So with fish in an uncycled tank, your test results show you are not changing enough water i.e. a trace of nitrite. This toxin has short and long term ramifications for your fish i.e. shortening their lives, even if the levels do not kill them outright.