The structural organization of water at a model of amorphous silica-liquid water interface is investigated by ab initio molecular dynamics (AIMD) simulations at room temperature. The amorphous surface is constructed with isolated, H-bonded vicinal and geminal silanols. In the absence of water, the silanols have orientations that depend on the local surface topology (i.e. presence of concave and convex zones). However, in the presence of liquid water, only the strong inter-silanol H-bonds are maintained, whereas the weaker ones are replaced by H-bonds formed with interfacial water molecules. All silanols are found to act as H- bond donors to water. The vicinal silanols are simultaneously found to be H- bond acceptors from water. The geminal pairs are also characterized by the formation of water H- bonded rings, which could provide special pathways for proton transfer(s) at the interface. The first water layer above the surface is overall rather disordered, with three main domains of orientations of the water molecules. We discuss the similarities and differences in the structural organization of the interfacial water layer at the surface of the amorphous silica and at the surface of the crystalline (0001) quartz surface.