What test kits are you confirming with. If API which I suspect, confirm by taking a water sample to a trusted LFS that does NOT use Api anything and see what readings they come up with and to compare with yours for confirmation.
IF and IF all checks out , you can sure add a couple of coral such as Zoa, candy cane, xenia, mushroom and even a small leather. Each of these have their own requirements but are forgiving BUT generally dont tolerate changes in water quality/spikes well hence the suggestion to confirm water quality.
With fish in the tank, you should be seeing some degree of ammonia and nitrate reading but API often shows Zero when its not.