Something to clarify that’s important
Live rock doesn’t need to cycle. It brings home all bac from the pet store. What we do with live rock is prevent free ammonia, but for dry rocks we add it
Polar opposite handling based on the kind of rock that is
Is that live rock above
Bottle bac is for dry rock cycling. Several ways to tell if you brought home skip cycle rocks that are already ready:
Was from a vat of water in the lfs marked live rock, has bugs and pods and starfish arms coming out the live rock. If it has algae or any living attachments that’s cycled rock.
Was the rock dry, or wet at the place you bought it? That and any attached growths are the final determinant. Post a clear, up close pic of the live rock. Per the pics above, it looks like there are attachments like algae and various growths. If that’s just dry life rock from Caribsea, painted, then it still doesn’t need bottle bac as you paid extra for rocks that have painted on bac.
Before anyone can advise your cycle we have to know rock specifics.
I have never seen purple rock that requires bottle bac one way or the other so odds are we are about to save you from wasting money. Knowing exactly how bacteria manifest in your reef tank is a critical first step in taking command over the system so you can care for it and clean it to prevent algae loss, your care boundaries are set by what bacteria allow so that’s why getting it right first pass matters. It starts you in a deliberate vs hesitating mode, that makes all the difference later on when invasive algae begins, you’ll already be practiced in matching the right action to a need vs a guess.