My point about the CPL/IR is that such level of proficiency will normally be expected before you commence a type rating course.
Actually, all FAA PIC type rating flight tests are conducted to ATP standards, regardless of the licence level the T/R is to be attached to.
For most advanced types, the training centre manager will want proof of total time, multi crew aircraft time, P1 time, jet time etc. if the centre's minimum times are not met, at the discression of the centre manager, you may be allowed to commence training and receive a T/R with a supervised operating experience or a SIC limitation.
Edit;
It's the aircraft insurance firms that practically set the minimums!