RESSET presents the last substantial methodological advance required for the application of SBI to realistic cosmological SN Ia samples: the ability to account for sample selection (and contamination, although not explicitly demonstrated here). To this end, it introduces set-based truncated autoregressive neural ratio estimation (STAR NRE), a simulation-based approach that makes use of a conditioned deep set neural network and combines efficient high-dimensional global inference with sub-sampling-based truncation in order to scale to very large survey sizes while training on sets with stochastic cardinality. Applying it to a simplified SN Ia model that consists of standardised brightnesses and redshifts with Gaussian uncertainties and a selection procedure based on the expected LSST sensitivity, we demonstrate precise and unbiased inference of cosmological parameters and the redshift evolution of the volumetric SN Ia rate from ≈100 000 mock SNæ Ia. Our method bypasses the latent layer and delivers marginal results, imposing no restrictions on the simulator’s output size (in fact, it naturally extracts useful information from it) and the nature of individual objects. It can thus handle an arbitrarily complicated selection and classification procedure and be applied to complex data like light curves in the future.