As others have commented, please fill in your "My Info" section with your specifics, because now we're going to start asking your about what type of filtration you have!
Sooo... if you don't have live rock, what type of filtration are you using? Biowheel? Wet/Dry? Your bacteria that will convert that ammonia to nitrites/nitrates need to live somewhere. They'll take up residence in your sand, but you really need another place for them to call home for efficient processing of the ammonia.
Yes... most folks cycle with live rock. If you don't add it now, you're going to end up with a cycle again anyway unless you get really "live" live rock. Is the "live" sand you're using from another tank that has been up for a while? Or is it the bagged "live" sand?
Not sure where your ammonia went. But if it was processed by bacteria in the live sand, then you should start seeing an increase in nitrates soon, if nothing else.