surface-Rb-doped TMDs[@KangNanoLett2017] highlighted the presence of a non-negligible spectral weight at the Q/Q’ valleys only for $n_{2d}\gtrsim8\cdot10^{13}$cm$^{-2}$ in the case of MoS$_2$. Thus, which valleys and sub-bands are involved in the gate-induced SC state still demands a satisfactory answer.

Here we report multi-valley transport and SC at the surface of liquid-gated FL-MoS$_2$. We use a dual-gate geometry to tune doping across a wide range of $n_{2d}\sim5\cdot10^{12}-1\cdot10^{14}$cm$^{-2}$, induce SC, and detect characteristic “kinks” in the transconductance. These are non-monotonic features that emerge in the $n_{2d}$-dependence of the low-temperature ($T$) conductivity when $E_F$ crosses the high-energy sub-bands[@BrummePRB2016], irrespectively of their specific effective masses, Fig.\[figure:bands\]e. We show that the population of the Q/Q’ valleys is fundamental for the emergence of SC. The crossing of the first sub-band Q$_1$ (Fig.\[figure:bands\]c) occurs at small $n_{2d}\lesssim2\cdot10^{13}$cm$^{-2}$, implying that multi-valley transport already occurs in the metallic phase over a wide range of $n_{2d}\sim2-6\cdot10^{13}$cm$^{-2}$. We also show that the crossing of the second sub-band Q$_2$ occurs after a finite $T_c$ is observed, while a full population of both spin-orbit-split sub-bands (Fig.\[figure:bands\]d) in the Q/Q’ valleys is required to reach the maximum $T_c$. These results highlight how SC can be enhanced in MoS$_2$ by optimizing the connectivity of its 