Investigations of multilayer structures based on superconducting and semiconductor films have recently gained particular interest due to the search for topological superconductors. The nature of the unexpected increase in the critical temperature in such superlattices is still a matter of debate. Possible sources include the unusual mechanism of Cooper pairing in such superstructures, the appearance of superconductivity in semiconductor layers, or amorphization of the interface region between two dissimilar films. In this work, we have studied Mo/Si nanolayer superlattices with the superconducting transition temperature between 7 and 8 K which were prepared by RF magnetron sputtering. Mesoscopic point contacts on them have been realized by bringing a sharp metallic tip of silver in touch with the sample surface. Using Andreev reflection spectroscopy for extracting the value of the superconducting order parameter, we have performed pointcontact measurements of the Mo/Si superlattices spectra well fitted with the Blonder-Tinkham-Klapwijk theory that assumes conventional s-wave ordering in the superconducting state. Our results show that the surprisingly high temperature of the normal-to-superconducting state transition in the Mo/Si superlattice is not related to any exotic mechanism but is rather connected with the formation of an amorphous alloy at the interfaces between Mo and Si layers. We believe that the main factor leading to the enhancement of superconducting characteristics is the emergence of soft vibrational modes in disordered Mo/Si interlayers and, as a result, the appearance of the so-called bosonic peak in the phonon spectra of the superlattices. The results obtained are expected to stimulate efforts for realizing silicon-based superconductive devices with farreaching application potential, in particular, in superconducting electronics.