What will happen if we start the A320 engines but we don't wait for the amber crosses on the E/WD to disappear?
Amber X's mean the FADEC is not yet energized. Once the X's disappear it means the FADEC is ready and can provide monitoring (even passive monitoring in a manual start).

Without FADEC there is no means to start the engine, as the valves are also FADEC controlled.

(A320 FADEC schematic.)

FADEC is needed even for manual start.