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We propose an alternative method to extract the leading-order hadronic contribution to the muon g−2, aμHLO, 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, Δαhad, in the space-like region, our approach relies on the computation of the derivatives of Δαhad(t) at zero squared momentum transfer t. We show that this approach allows to extract ∼99% of the total value of aμHLO from the MUonE data, while the remaining ∼1% can be computed combining perturbative QCD and data on e+e− annihilation to hadrons. This leads to a competitive evaluation of aμHLO which is robust against the parameterization used to model Δαhad(t) in the MUonE kinematic region, thanks to the analyticity properties of Δαhad(t), which can be expanded as a polynomial at t∼0.