We propose an alternative method to extract the leading-order hadronic contribution to the muon $g-2$, $a_{\mu }^{\text{HLO}}$, with the MUonE experiment. In contrast to the traditional method based on the integral of the hadronic contribution to the running of the electromagnetic coupling, $\Delta {\alpha }_{had}$, in the space-like region, our approach relies on the computation of the derivatives of $\Delta {\alpha }_{had}\left(t\right)$ at zero squared momentum transfer t. We show that this approach allows to extract $\sim 99\text{\%}$ of the total value of $a_{\mu }^{\text{HLO}}$ from the MUonE data, while the remaining $\sim 1\text{\%}$ can be computed combining perturbative QCD and data on $e^{+}{e}^{-}$ annihilation to hadrons. This leads to a competitive evaluation of $a_{\mu }^{\text{HLO}}$ which is robust against the parameterization used to model $\Delta {\alpha }_{had}\left(t\right)$ in the MUonE kinematic region, thanks to the analyticity properties of $\Delta {\alpha }_{had}\left(t\right)$, which can be expanded as a polynomial at $t\sim 0$.