Recent developments in manufacturing require holes on composite materials, especially on the carbon fiber reinforced polymer (CFRP) with smooth hole periphery, low delamination, burr formation, taper, better circularity, and a high processing speed. Its non-conductive surface (epoxy layering) limits its machining through electrical discharge machining (EDM). To overcome this limitation, an aluminum fixture has been designed to guide the copper electrode of EDM for producing holes on a CFRP sheet of 1 mm thickness at low machining complexity, cost, time, delamination, burr in hole periphery and without affecting the material’s surface quality and performance. Even components with high geometrical complexity can also be drilled through this approach. Here, a multi-quality analysis called grey relational analysis is developed for examining the hole quality attributes, considering peak current, pulse on and off time, and flushing pressure as input parameters. This approach points out the optimum factor level setting and critical parameters (pulse-on time and peak current) that regulate the hole attributes (entrance and exit diameter, circularity, taper, material removal, and tool wear rate). An artificial neural network model has been designed and trained through experimental data sets. This model can also be adopted during the determination of hole quality attributes when the parameter settings are beyond a defined boundary, as the regression analysis value is very close to 1, and model performance is 4.99e-10. Peak current = 4 A, pulse-on time = 25 µs, pulse-off time=25 µs, and flushing pressure = 0.6 MPa were the optimum drilling parameters. In the initial hole, average burr length is 391.75 μm, and delamination of 539.3 μm is noticed. But burr formation is very negligible with delamination of 350.7 μm being observed with uniform circularity (0.979), low taper angle (−0.81354°), and TWR (0.000069 g/min) under optimum drilling conditions through this drilling approach.