If everything is "dead" then there is no need to "cycle" the tank. Cycling is the process of cultivating the appropriate populations of bacteria to process ammonia, (from rotting substances), and Nitrites which is the byproduct of the Ammonia being processed. If you have no organic matter in the tank then there will be no production of ammonia and thus no production of bacteria.
Were you to place a cocktail shrimp in there for example your tank will cycle and produce the required populations of the aforementioned bacteria. However, if you then left the tank with no organics, (ie: no creatures), then the populations would die off back to zero. If you were to place a small fish in there after cycling with the shrimp the populations would still die off but only to a point where they can survive on the organic waste from the fish and any uneaten food, (bacteria are living creatures that require food too and they live on ammonia).
Now, before you go rushing out and purchasing your first 100 fish
because you don't need to cycle the tank.... Don't!!! The sudden large influx of organics will cause a cycle that will probably be deadly to the livestock. Adding animals, (small ones), one at a time and leaving at least a week, preferably two, between additions will allow the cycle to take place in such a way that it adjusts to the current organic levels without being detrimental to the inhabitants.
But I notice you have some live base rock and some live sand. There will be some small die off, (assuming proper transportation otherwise the die off could be large), in those when you add them to the tank yet the base rock will already have some small populations of the appropriate bacteria so the time required to balance the die off to the appropriate populations would be short.
I would recommend placing the rock and sand - if it has been well transported - into the tank and leaving it for a week. Then begin adding the fish you want one at a time and waiting at least a week between fish being careful to take note of their size and, since you are adding fish, their interaction with others which might affect the order that you add them. (You don't want to put that spiffy 6" Sohal Tang in before you put your Emperor Angel in...
)