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We introduce AutoEnRichness, a hybrid approach that combines empirical and analytical strategies to determine the richness of galaxy clusters (in the redshift range of $0.1 \leq z \leq 0.35$) using photometry data from the Sloan Digital Sky Survey Data Release 16, where cluster richness can be used as a proxy for cluster mass. In order to reliably estimate cluster richness, it is vital that the background subtraction is as accurate as possible when distinguishing cluster and field galaxies to mitigate severe contamination. AutoEnRichness is comprised of a multi-stage machine learning algorithm that performs background subtraction of interloping field galaxies along the cluster line-of-sight and a conventional luminosity distribution fitting approach that estimates cluster richness based only on the number of galaxies within a magnitude range and search area. In this proof-of-concept study, we obtain a balanced accuracy of $83.20$ per cent when distinguishing between cluster and field galaxies as well as a median absolute percentage error of $33.50$ per cent between our estimated cluster richnesses and known cluster richnesses within $r_{200}$. In the future, we aim for AutoEnRichness to be applied on upcoming large-scale optical surveys, such as the Legacy Survey of Space and Time and $\textit{Euclid}$, to estimate the richness of a large sample of galaxy groups and clusters from across the halo mass function. This would advance our overall understanding of galaxy evolution within overdense environments as well as enable cosmological parameters to be further constrained.