Over the past two decades, multiple astroparticle physics experiments have observed an excess of muons in air shower measurements compared to predictions based on hadronic interaction models calibrated to LHC data. This discrepancy impacts the interpretation of mass composition studies and has deep implications regarding our understanding of hadronic processes at the highest energies. In this work, a Monte Carlo simulation method is proposed, where the longitudinal profiles of simulated and observed air showers are matched in order to estimate the quantity by which the muon content and the Heitler-Matthews $\beta$ coefficient of a given model must be adjusted to describe the input data. This so-called "Top-Down" method is tested with a mockup dataset composed of air showers simulated at 10 EeV with the Sibyll$\star$ model, for different primaries, and reconstructed with the Pierre Auger Observatory software. Assuming the mass composition fraction measured by the Pierre Auger Observatory at this energy for the Sibyll 2.3d model, the quality of the recovery of the muon signal of the mockup dataset is investigated.