Seismological models from Apollo missions provided the first records of
the Moon inner structure with a low-velocity zone (LVZ) at the bound-
ary between the core and the mantle. In addition, the resolution of
these records prevent a strict detection of a putative lunar solid inner
core and the impact of the lunar mantle overturn in the lowest part
of the Moon is still discussed. Our work combines geophysical and
geodesic constraints from Monte-Carlo exploration and thermodynam-
ical simulations for different Moon internal structures. We show that
only models with ilmenite-rich LVZ and an inner core present densities
deduced from thermodynamic constraints compatible with densities
deduced from tidal deformations. We thus obtain strong indications
in favour of the lunar mantle overturn scenario and in this context,
demonstrates the existence of the lunar inner core with a radius of (258
± 40 km) and density (7,822 ± 1,615 kgm3). Our results question the
evolution of the Moon magnetic field thanks to its demonstration of
the existence of the inner core and supports a global mantle overturn
scenario that brings significant insights on the timeline of the lunar
bombardment in the first Gyr of the Solar System.