Even just a little live rock should have all the bacteria you need, and if you use enough of it (50%-100%), that can result in basically an "instantly cycled" tank, where you could theoretically add fish and live stock right away. In practice, and from experience, I'd exercise a little more care that that, but that's the theory; the live rock is already cycled. Cycled and cured are synonymous when speaking of the beneficial bacteria and the rock as a bio filter - both would be good choices to start your tank.
Keep in mind you can place small pieces of live rock rubble in a section of your AIO, I do this on my 25 gallon AIO. Even some rock rubble will have all kinds of bacteria on it, it can really jump start your tank, in my experience.
I will say there are those here on R2R that absolutely do prefer to use dry rocks, sand, and bottled bacteria. I've done that, many people do it, but having also used live rock I can say that using live rock results in a more interesting and better looking tank much more quickly than using dry rocks. That's just my opinion, both methods work, and certainly dry rock is cheaper. A lot of people do say that using dry rock results in a longer "ugly phase" of a new tank, but others suggest that's not always true.
I'm going to say if this is your first tank, I would just turn the lights on and enjoy your tank. Most new reefers don't want to look at a dark tank of white rocks for several months. "Uglies" will come and go and can be dealt with. I recently did a nearly three month dark start on my most recent tank, but here I'm going to suggest you not worry about that, and just start enjoying your tank. Most new reefers can barely make it through a three week cycle without adding a Clownfish