I think it’s necessary to differentiate between two apparently similar statements: “Science studies only physical phenomena,” and “Science is the study of physical phenomena.”
By its self-imposed limitations, science does not study the whole of physical reality, but only patterns of regularity within it, made into abstractions in order to predict other similar events.
Quite apart from the strength or weakness of design arguments, design is about contingency: to design a trombone and to design a constitution are very different things, though executed by, potentially, the same human mind. It is therefore quite possible - if not inevitable - for divine design to be opaque to scientific examination.
If it can be mathematicized, it is no longer design that is being considered, but something else (such as what there is in common between the design of a trombone and the design of a constitution once one ignores the artifacts themselves).