A better understanding of greenhouse gas surface sources and sinks is required in order to address the global challenge of climate change. Space-borne remote estimations of greenhouse gas atmospheric concentrations can offer the global coverage that is necessary to improve the constraint on their fluxes, thus enabling a better monitoring of anthropogenic emissions. In this work, we introduce the Adaptable 4A Inversion (5AI) inverse scheme that aims to retrieve geophysical parameters from any remote sensing observation. The algorithm is based on the Optimal Estimation algorithm, relying on the Operational version of the Automatized Atmospheric Absorption Atlas (4A/OP) radiative transfer forward model along with the Gestion et Étude des Informations Spectroscopiques Atmosphériques: Management and Study of Atmospheric Spectroscopic Information (GEISA) spectroscopic database. Here, the 5AI scheme is applied to retrieve the column-averaged dry air mole fraction of carbon dioxide (XCO2) from a sample of measurements performed by the Orbiting Carbon Observatory-2 (OCO-2) mission. Those have been selected as a compromise between coverage and the lowest aerosol content possible, so that the impact of scattering particles can be neglected, for computational time purposes. For air masses below 3.0, 5AI XCO2 retrievals successfully capture the latitudinal variations of CO2 and its seasonal cycle and long-term increasing trend. Comparison with ground-based observations from the Total Carbon Column Observing Network (TCCON) yields a bias of 1.30±1.32gppm (parts per million), which is comparable to the standard deviation of the Atmospheric CO2 Observations from Space (ACOS) official products over the same set of soundings. These nonscattering 5AI results, however, exhibit an average difference of about 3gppm compared to ACOS results. We show that neglecting scattering particles for computational time purposes can explain most of this difference that can be fully corrected by adding to OCO-2 measurements an average calculated-observed spectral residual correction, which encompasses all the inverse setup and forward differences between 5AI and ACOS. These comparisons show the reliability of 5AI as an optimal estimation implementation that is easily adaptable to any instrument designed to retrieve column-averaged dry air mole fractions of greenhouse gases.