The formation of supported lipid bilayers (SLB) on hydrophilic substrates through the method of unilamelar vesicle fusion is used routinely in a wide range of biophysical studies. In an effort to control and better understand the fusion process on the substrate, many experimental studies employing different techniques have been devoted to the elucidation of the fusion mechanism. In the present work, we follow the kinetics of membrane formation using time-resolved (TR) neutron reflectivity, focusing on the structural changes near the solid/liquid interface. A clear indication of stacked bilayer structure is observed during the intermediate phase of SLB formation. Adsorbed lipid mass decrease is also measured in the final stage of the process. We have found that it is essential for the analysis of the experimental results to treat the shape of adsorbed lipid vesicles on an attractive substrate theoretically. The overall findings are discussed in relation to proposed fusion mechanisms from the literature, and we argue that our observations favor a model involving enhanced adhesion of incoming vesicles on the edges of already-formed bilayer patches.