By the term cycling one means providing an environment and seeding/planting beneficial bacteria to allow that bacteria to grow to a sufficient population to safely consume harmful ammonia into substances safe for fish and corals to live in. Part of that environment is providing saltwater with suitable parameters, first and foremost with a salinity in the range of 1.024-1.026 ideally and a temperature somewhere between 78 and 80° F. The second part is seeding the tank with bacteria, either from a bottle or from "live rock" or existing aquarium filtration substrate (if a fellow hobbyist or petstore is kind enough to have this).
Only once you have your saltwater at these two parameters should you either add live rock or bottled bacteria to start the cycling process. I hope that, via a long about way, answers your question?
The cycling process can take a varying amount of time. If you have healthy live rock transported in a short amount of time in water such that little of the organisms on it die off, you can have a stable environment very quickly. Take the same live rock with some live organisms dying (due to a longer transport time or being shipped in paper with less stable temperatures), and that dead material may exceed the existing bacteria's ability to neutralize the ammonia. (The bacteria is located on the surface of and in the interior pores of the rock). Clearly that will take a bit more time to establish the correct bacteria population to neutralize the ammonia created by the increased load from the dying material. If you start with sterile dry rock that has never been exposed to a salt water environment (or rock that was previously in a tank but has since long dried out) the process could take many weeks. When I first started very sterile tanks back in the 1980's, it took roughly 6 weeks to see test kits show stable ammonia and nitrite levels. That can certainly be accelerated through more modern use of live rock and bottled bacteria. There is a lot more material available on this....I recommend looking at the beginner's forum here on Reef2Reef.