Layers of transition metal dichalcogenides (TMDs) combine the enhanced effects of cor- relations associated with the two-dimensional limit with electrostatic control over their phase transitions by means of an electric field. Several semiconducting TMDs, such as MoS2, de- velop superconductivity (SC) at their surface when doped with an electrostatic field, but the mechanism is still debated. It is often assumed that Cooper pairs reside only in the two electron pockets at the K/K’ points of the Brillouin Zone. However, experimental and theoretical results suggest that a multi-valley Fermi surface (FS) is associated with the SC state, involving 6 elec- tron pockets at the Q/Q’ points. Here, we perform low-temperature transport measurements in ion-gated MoS2 flakes. We show that a fully multi-valley FS is associated with the SC onset. The Q/Q’ valleys fill for doping& 2 · 1013cm−2, and the SC transition does not appear until the Fermi level crosses both spin-orbit split sub-bands Q1 and Q2. The SC state is associated with the FS connectivity and promoted by a Lifshitz transition due to the simultaneous population of multiple electron pockets. This FS topology will serve as a guideline in the quest for new superconductors.