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We investigate cosmological dynamics in the Einstein-Gauss-Bonnet gravity using the effective potential. The model under consideration includes a scalar field, that is non-minimally coupled to both with the Ricci scalar and the Gauss-Bonnet curvature invariant. We derive conditions for stable de Sitter solutions via the effective potential. Specializing in specific couplings, we explore the possibility of realizing the stable de Sitter configurations which may have implications for both the early Universe and late-time evolution. In particular, we express the observable inflationary parameters via derivatives of the effective potential. The talk is based on the following papers: E.O. Pozdeeva, M. Sami, A.V. Toporensky, S.Yu. Vernov, Phys. Rev. D 100 (2019) 083527 and E.O. Pozdeeva, M.R. Gangopadhyay, M. Sami, A.V. Toporensky, S.Yu. Vernov, Phys. Rev. D 102 (2020) 043525.