There's nothing wrong with having carbon when you cycle, it won't hurt the cycle and won't adsorb ammonia. In fact carbon is technically a pretty good surface media for growing the beneficial bacteria. The problem, and the thing that makes it far from ideal as a biomedia is that it crumbles, getting smaller and smaller and eventually both the carbon dust and the bacteria on that go out during a filter cleaning. By comparison, sponges, ceramic rings, ceramic pebbles and bioballs are a much better choice as a biomedia.
Now, that having been said, what is carbon good for? Carbon is not meant to be a biological media choice, instead its a "chemical media" and its job is to "adsorb" or collect chemicals based on molecular charge. Its used to clear medicines, to clear yellow tannins from bogwood and to clear the occasional organic smell that's unexplained. So its an excellent tool for the hobbyist, but its meant to be stored on the shelf and just used when you have these needs. When you add it to your filter and put it to work it will adsorb for about 3 days and then its ready to be removed and tossed. During the vast majority of time you're running your tank, there's no need to have carbon in the filter.
Why do the manufacturers add it to your new filter? Well, its one of those wonderful "gray-zone" products for them. Its a genuine good thing and so can't be faulted, but many beginners misunderstand it and so will fall for the idea that they need to buy it on a regular basis and keep using it, thus providing steady revenue to the companies. They same sort of misunderstading is used for filter "cartridges," in an attempt to give the feeling that they should be replaced, when in fact that's not what's really needed in a filter.
You say you're doing the "wait method" by which I hope you mean the add&wait method as that's the one we most often recommend. It can sometimes take up to two weeks to see the initial 5ppm of ammonia that you first added drop to zero, but usually its faster than that. So you have to be very patient. As long as you've got some disturbance of the water surface to encourage oxygenation and a good water flow through the filter, the A-Bacs (ammonia oxidizing bacteria) should eventually show up. An ideal temp is 29C/84F and the best pH is 8.0-8.4. You want to be measuring ammonia and pH about once a day initially and recording in your aquarium log. Hopefully you've already got a good liquid-reagent based testing kit?
~~waterdrop~~