Note that it is not "me who is trying", but more the work of an entire community :)
After this side note, let's go back to your question. The collision parameters are fixed. We know the LHC energy, we know what we collide and we know how many collisions are recorded on disk. Then the rest is to define criteria allowing to select a subset of these collisions, and to make sure that any signal would be included in the selection together with as few Standard Model background as possible.
From the non-observation of any signal through this selection (as there is no sign of new physics in data so far), we can draw conclusive statements on the nature of any potential signal.
Does it clarify?
RE: Compositeness as a potential theory for new particle physics phenomena