There are factors that determine how quickly the nitrifiers settle in and begin colonizing the media/surfaces. Temperature is a big factor, so cooler systems (like in Aquaculture, Lobster Systems, cold water exhibits in public aquaria) take longer. Water quality, does the water contains the things the nitrifiers need (alk, phosphates, trace elements, etc.) and nothing inhibiting them (Copper, etc.). Other things like flow, dissolved oxygen, amount of suitable media, etc. No two systems are exactly the same.
I am curious, and again more just to file under *this is interesting for me* if aside from temperature since most of us don’t deal with cold water systems, if the water quality and parameters such as DO and media, while undoubtedly having an impact, have such an impact a hobbiest would find it meaningful when it comes to attachment times. Is it a 5x longer process to attach if one doesn’t have ceramic media or just a few hours for example. Now those sorts of questions are more in depth to test and are really out of scope for this, but interesting to me at least. Even attachment time to ceramic, vs calcium carbonate (live rock) vs glass are going to be different, but are they different enough to have a meaningful impact, such has hours vs days.