A flexible and robust simulation-based framework is introduced to infer demographic parameters from the site frequency spectrum (SFS) of large genomic datasets. The method uses a composite-likelihood approach based on coalescent simulations, allowing for the analysis of complex evolutionary models that are not feasible with current likelihood-based methods. It outperforms the widely used δaδi method in terms of convergence and accuracy for complex models, while maintaining comparable performance for simpler scenarios. The framework is applied to non-coding SNP data from four human populations, revealing demographic history and divergence times between populations. It is also extended to handle ascertained SNP panels, such as those from Affymetrix, allowing for the inference of parameters in complex models involving multiple populations, bottlenecks, and migration. The method is tested on simulated data and applied to real data, showing accurate estimation of demographic parameters, including divergence times between African populations. The results suggest an ancient divergence between Yoruba and San populations. The method is robust, efficient, and applicable to a wide range of demographic models, making it a valuable tool for studying complex evolutionary scenarios from large genomic datasets.A flexible and robust simulation-based framework is introduced to infer demographic parameters from the site frequency spectrum (SFS) of large genomic datasets. The method uses a composite-likelihood approach based on coalescent simulations, allowing for the analysis of complex evolutionary models that are not feasible with current likelihood-based methods. It outperforms the widely used δaδi method in terms of convergence and accuracy for complex models, while maintaining comparable performance for simpler scenarios. The framework is applied to non-coding SNP data from four human populations, revealing demographic history and divergence times between populations. It is also extended to handle ascertained SNP panels, such as those from Affymetrix, allowing for the inference of parameters in complex models involving multiple populations, bottlenecks, and migration. The method is tested on simulated data and applied to real data, showing accurate estimation of demographic parameters, including divergence times between African populations. The results suggest an ancient divergence between Yoruba and San populations. The method is robust, efficient, and applicable to a wide range of demographic models, making it a valuable tool for studying complex evolutionary scenarios from large genomic datasets.