Is it possible to become an FI without having a CPL, then using the hours gained as an FI to get a CPL (Seems like a cheaper option to me
In what way is it cheaper?
You still need 150 hours PIC to become a flying instructor, so no money saved there.
You need to do CPL(A) theory. The more common route is to do ATPL theory, do the CPL(A) (with or without IR(A)) and then do the FI(A).
With ATPL groundschool you have to get BOTH the CPL and the IR within three years of the last exam, or the exams expire, so unless you are very sure of your timeline on getting CPL and IR, you could end up repeating groundschool, which will cost you even more.