The inputs to the A4988 driver you show are STEP and DIRECTION, It is possible to use two wires of the "4-in"/quadrature signals to drive a STEP-DIR driver, since one wire can serve as DIR while a wire in quadrature to it serves as DIR.
Here are the "4-in" signals from Stepper.h:
You could drive the STEP+DIR inputs wirth the C1+C2 pair or the C0+C3 pair--the trick is you need to step the 4 times with Steppr.h to deliver a full cycle to the driver's the STEP pin.