Well your sand bed is were the bacteria u want in your tank to break down the ammonia into nitrite then from nitrite into nitrate live.so having a DSB is the best thing because it's your biological filter for ur tank the hang on the back filter is really only good for taking some of the physical things out of your water the carbon that also usually come it takes some toxic things that is usually from your hands and stuff that's on your hand out to. And also the live rock is another natural filter the organisms u find in your live sand is also in the live rock you get but make sure it's live rock not base rock. But it takes awhile for all these organism u want in your tank to grow but as I said there are ways to speed it up like buying live rock from well established tank and u will get these organism with the live rock or live sand u get from that tank just put it in your tank and it will take off. They multiple fast and this I think is one of the best ways to ether start or so called ( speed up your cycle process) I don't know if people advise this but I know it's working for me so far everything in my tank is doing great I haven't had a spike at all and I have yet so do a water change but there are other factors that helps also with my tank to get like that. But also my tank is new may have problems in future but until I see problems I will keep my tank this way.
Lol sorry for mixing things up hopefully u understand it