The space elevator construction begins with its initial cable deployment. In this paper, the feasibility of the space elevator initial cable deployment system is investigated through numerical system analysis. During the initial cable deployment, the orbit of the space elevator must be controlled to be geostationary to avoid any conflict with other GEO satellites. This orbital control becomes the constraint to determine the total mass of the initial cable deployment system and the required time to complete the full cable deployment. Through the system analysis assuming the use of the ion thruster or bipropellant thruster, it is found that the total fuel for the orbital control decreases as the main satellite mass increases. It is also found that the main satellite mass has the optimum value to minimize the total mass in the case of the bipropellant thruster. As the initial cable does not have sufficient strength and survivability against debris, its deployment time should be minimized. The deployment time analysis has clarified it is possible to complete the full deployment of the initial cable in about 5 days in both the ion and bipropellant thruster cases. The feasible configuration of the initial cable deployment system is clearly presented.