The interfacial Dzyaloshinskii-Moriya Interaction (iDMI) is an antisymmetric exchange interaction that is induced by the broken inversion symmetry at the interface of, e.g., a ferromagnet/heavy metal. Thus, the presence of iDMI is not expected in symmetrical multilayer stacks of such structures. Here, we use thermal annealing to induce the iDMI in a [Py/Pt](x10) symmetrical multilayer stack. Brillouin light scattering spectroscopy is used to directly evidence the iDMI induction in the annealed sample. Structural characterizations highlight the modified crystallinity as well as a higher surface roughness of the sample after annealing. First principles electronic structure calculations demonstrate a monotonic increase of the iDMI with the interfacial disorder due to the interdiffusion of atoms, depicting the possible origin of the induced iDMI. The presented method can be used to tune the iDMI strength in symmetric multilayers, which are the integral part of racetrack memories, magnonic devices as well as spin-orbitronic elements.