Context. Coronal mass ejections (CMEs) stand as intense eruptions of magnetized plasma from the Sun, and they play a pivotal role in driving significant changes of the heliospheric environment. Deducing the properties of CMEs from their progenitors in solar source regions is crucial for space weather forecasting. Aims. The primary objective of this paper is to establish a connection between CMEs and their progenitors in solar source regions, enabling us to infer the magnetic structures of CMEs before their full development. Methods. We created a dataset comprising a magnetic flux rope series with varying projection shapes (S-, Z-, and toroid-shaped), sizes, and toroidal fluxes using the Regularized Biot-Savart Laws (RBSL). These flux ropes were inserted into solar quiet regions with the aim of imitating the eruptions of quiescent filaments. Thereafter, we simulated the propagation of these flux ropes from the solar surface to a distance of 25 R_⊙ with our global coronal magnetohydrodynamic (MHD) model COCONUT. Results. Our parametric survey revealed significant impacts of source flux ropes on the consequent CMEs. Regarding the flux-rope morphology, we find that the projection shape (e.g., sigmoid or torus) can influence the magnetic structures of CMEs at 20 R_⊙, albeit with minimal impacts on the propagation speed. However, these impacts diminish as source flux ropes become fat. In terms of toroidal flux, our simulation results demonstrate a pronounced correlation with the propagation speed of CMEs as well as the successfulness in erupting. Conclusions. This work builds the bridge between the CMEs in the outer corona and their progenitors in solar source regions. Our parametric survey suggests that the projection shape, cross-section radius, and toroidal flux of source flux ropes are crucial parameters in predicting magnetic structures and the propagation speed of CMEs, providing valuable insights for space weather prediction. On the one hand, the conclusion drawn here could be instructive in identifying the high-risk eruptions with the potential to induce stronger geomagnetic effects (B_z and propagation speed). On the other hand, our findings hold practical significance for refining the parameter settings of launched CMEs at 21.5 R_⊙ in heliospheric simulations, such as with EUHFORIA, based on observations for their progenitors in solar source regions.