To retrieve aerosol properties from satellite measurements of the oxygen A-band in the near-infrared, a line-by-line radiative transfer model implementation requires a large number of calculations. These calculations severely restrict a retrieval algorithm's operational capability as it can take several minutes to retrieve the aerosol layer height for a single ground pixel. This paper proposes a forward modelling approach using artificial neural networks to speed up the retrieval algorithm. The forward model outputs are trained into a set of neural network models to completely replace line-by-line calculations in the operational processor. Results comparing the forward model to the neural network alternative show an encouraging outcome with good agreement between the two when they are applied to retrieval scenarios using both synthetic and real measured spectra from TROPOMI (TROPOspheric Monitoring Instrument) on board the European Space Agency (ESA) Sentinel-5 Precursor mission. With an enhancement of the computational speed by 3 orders of magnitude, TROPOMI's operational aerosol layer height processor is now able to retrieve aerosol layer heights well within operational capacity.