Using gradient- and dispersion-corrected density functional theory in connection with ab initio molecular dynamics and efficient, parametrized Velocity-Velocity Autocorrelation Function (VVAF) methodology, we study the vibrational spectra (Vibrational Sum Frequency, VSF, and infrared, IR) of hydroxylated α-Al2O3(0001) surfaces with and without additional water. Specifically, by considering a naked hydroxylated surface and the same surface with a particularly stable, "ice-like" hexagonal water later allows us to identify and disentangle main spectroscopic bands of OH bonds, their orientation and dynamics, and the role of water adsorption. In particular, we assign spectroscopic signals around 3700 cm-1 as being dominated by perpendicularly oriented non-hydrogen bonded aluminol groups, with and without additional water. Furthermore, the thin water layer gives spectroscopic signals which are already comparable to previous theoretical and experimental findings for the solid/(bulk) liquid interface, showing that water molecules closest to the surface play a decisive role in the vibrational response of these systems. From a methodological point of view, the effects of temperature, anharmonicity, hydrogen-bonding, and structural dynamics are taken into account and analyzed, allowing us to compare the calculated IR and VSF spectra with the ones based on normal mode analysis and vibrational density of states. The VVAF approach employed in this work appears to be a computationally accurate yet feasible method to address the vibrational fingerprints and dynamical properties of water/metal oxide interfaces.