Coronal mass ejections (CMEs) and solar flares are the main drivers of weather in space. Understanding how these events occur and what conditions might lead to eruptive events is of crucial importance for up to date and reliable space weather forecasting. The aim of this paper is to present a numerical magnetohydrodynamic (MHD) data-inspired model suitable for the simulation of the CME initiation and their early evolution. Starting from a potential magnetic field extrapolation of the active region (AR) NOAA 9415, we solve the full set of ideal MHD equations in a non-zero plasma-β environment. As a consequence of the applied twisting motions, a force-free-magnetic field configuration is obtained, which has the same chirality as the investigated AR. We investigate the response of the solar corona when photospheric motions resembling the ones observed for AR 9415 are applied at the inner boundary. As a response to the converging shearing motions, a flux rope is formed that quickly propagates outward, carrying away the plasma confined inside the flux rope against the gravitational attraction by the Sun. Moreover, a compressed leading edge propagating at a speed of about 550 km s-1 and preceding the CME is formed. The presented simulation shows that both the initial magnetic field configuration and the plasma-magnetic-field interaction are relevant for a more comprehensive understanding of the CME initiation and early evolution phenomenon.