This type of floor can be cut, but you have to know what you are getting into and provide additional support as needed. The best approach would be to contact the producer who supplied the floor for guidance. These are engineered, structural systems that assume certain things about the supports and continuity of the floor panels. The original producer would know what these assumptions were and how to accommodate the church’s needs. Alternatively the church could hire a consulting structural engineer.
Precast producers do provide reference materials for their products. For example, Spancrete provides guidelines for cutting small penetrations (up to 10 inches) online at www.spancrete.com/pdfs/spanNotes/spanNotes9.pdf. It includes hints on planning the cut and the very important note that you should not cut reinforcing strands without permission of the manufacturer unless shown on the approved shop drawings.
If you were talking about a small hole to accommodate a hydraulic cylinder, that might be all the guidance you would need. But an elevator will obviously require a hole larger than 10 inches. And in that case, an engineering analysis will be required.