There's a cycling thread here on page two available that says live rock is already cycled and needs no bacteria nor ammonia added to keep it ready, as long as you want to wait. I noticed that key detail hadn't been covered, it rarely is covered in current cycling materials
You mentioned having live rock, I'd add it, then plan for fallow/quarantine procedure before adding fish, so they won't die. Amazing side benefit of 76 day fallow=cycling time.
If you add the live rock and the dry+ live sit together until January, then by association the dry materials are cycled.
You would be amazed at how much bacteria build up on your dry surfaces simply by filling saltwater and waiting till January, the water itself you make up always has nitrifers already in it. It's not possible to set up an aquarium in a home and not import nitrifiers, they're part of home biota and will cross contaminate.
Bottle bac purchasing is for beating time constraints, they're not required. You can fill a tank, leave it alone, and it still cycles anyway. In the 80s we did it this way, before the bottle bac phase of the hobby, the phase designed to misrepresent the need for purchasing bac and what bacteria need to survive so that money leaves one set of pockets and moves into another
I still do this in freshwater setups regularly, unassisted cycling. and I've used quick cycle products too so I didn't have to wait on other projects. It's easy to cycle your dry materials independent of the live rock as well if you want to. Fill the tank, dump in any brand of bottle bac and a pinch of food and wait forty days/done, and you don't even have to test for anything, this always works.