The Cultural Transmission of Reproductive Success (CTRS) is one of the various cultural processes that can impact human genetic evolution. In this process, individuals from large families have more children on average. Here, we develop and evaluate methods to infer this process from genomic data, using two approaches: (1) Approximate Bayesian computation, which uses summary statistics computed on inferred genealogies from genomic data and (2) deep neural networks, which are directly trained on genomic data. These methods rely on large simulated datasets incorporating varying levels of CTRS. Both competing approaches show a good ability to infer CTRS on genomic data and worth investigating under more complex evolutionary histories.