The properties of the Inconel 718 superalloy are used in the manufacturing of aircraft components; its properties, including high hardness and toughness, cause machining difficulties when using the conventional method. To circumvent this, non-conventional techniques are used, among which electrical discharge machining (EDM) is a good alternative. However, the nature of removing material using the EDM process causes the thermophysical properties of Inconel 718 to hinder its machinability; thus, a more extensive analysis of the influence of these properties on the EDM process, and a machinability analysis of this material in a wider range, using more process parameters, are required. In this study, we investigated the drilling of micro-holes into the Inconel 718 superalloy using the EDM process. An experiment was conducted to evaluate the impact of five process parameters with a wide range of values (open voltage, time of the impulse, current amplitude, the inlet dielectric fluid pressure, and tube electrode rotation) on the process’s performance (drilling speed, linear tool wear, the side gap thickness, and the aspect ratio of holes). The analysis shows that the thermal conductivity of this superalloy significantly influences the effective drilling of holes. The combination of a higher current amplitude (I ≥ 3.99 A) with an extended pulse time (ton ≥ 550 µs) can provide a satisfactory hole accuracy (side gap thickness ≤ 100 µm), homogeneity of the hole entrance edge without re-solidified material, and a depth-to-diameter ratio of about 19. Obtaining a high dimensional shape accuracy of holes has an enormous effect on their usability in the structure of the components in the aviation industry.