The direct growth of graphene via chemical vapour deposition on dielectric materials is a promising approach for transfer-free applications. However, large-scale production using this technique is hindered by the slow growth on non-catalytic substrates. In this study, the growth mechanism of graphene on glass fibre is theoretically explored, assuming α-SiO₂(001) as the model substrate. C₂/C₂H (from ethylene and acetylene) and C₃/C₃H (from propane) are identified as the active species driving the growth process. C₂H and C₃ are also key for nucleation because of their excellent migration capabilities. In hydrogen-passivated surface models, C₂H demonstrates a lower energy barrier for growth. Experimental results further indicate that acetylene, ethylene, and propane are promising carbon sources for graphene synthesis. These results are valuable for understanding the synthesis of graphene-skinned glass fibre fabrics, with the potential to improve graphene production on insulating substrates.