In case anyone was interested in learning more about the nitrogen cycle in depth and how it is not as simple or linear as we think, (IE NH3-N04-N03-N2) check out an older article on here on Reefs.com. While it is geared towards reef aquaria, the same process happens in freshwater aquaria.
As far as having zero nitrates on a cycled aquarium being unlikely, that is clearly not the case or even difficult to achieve. I’ve never registered nitrates on my 135G because I use lots of porous media (Eheim substrat pro and biohome ultimate) in my canister filters. I utilize no live plants in this aquarium and feed my large fish heavily. The anaerobic bacteria simply convert nitrates to nitrogen gas. You just need to have enough dense, porous media to provide ample space for these anaerobic bacteria to grow.