 If one doesn’t interpret the model purely mathematically, but instead considers what phenomenon the Hardy-Weinberg Principle with-finite-populations is seeking to model, then there is indeed a larger population being sampled. The equation models the changes from one generation to the next; the original generation is the population that is being sampled, and the next generation is the “sample”. That sample may or may not be representative of the original population, e.g., a heterozygote Aa of the original generation may or may not have offspring in the proportions 25% AA, 50% Aa, and 25% aa.