The article is picking up new methodological approaches to the study of the Сosmos and the understanding of the place of a human being in the Universe. The article has a methodological character and is presented in the form of the analysis and synthesis of various aspects of the study of this problem. The article considers theoretical and methodological aspects of cosmology, the analysis of modern scientific theories, the scope of their applicability. The obtained outputs can be used in cosmological modeling and in the studies of anthropological and existential aspects of cosmology. The authors conclude that there is only nondirective proof of the study of calculated predictions when investigating the early stages of the evolution of the Universe. Theorists simulate the processes of evolution of the Universe and compare the simulation results with the available empirical data. There is a possibility to change initial conditions within certain limitations to obtain the outer facts. The extrapolation of Friedmann model at earlier stages of the evolution of the Universe is permissible only up to certain limits, whereupon "normal" laws fail and abstract formulas remain, which critically do not accept experimental verification. Neither of modern relativistic cosmological theories erase a problem of the anthropic principle, i. e. they do not respond to a question of the place of a human being in the Universe.