For a Hermitian complex manifold endowed with a positive line bundle, Tian's approximation theorem asserts that, considering the large tensor powers of the line bundle, the sequence of Fubini-Study metrics induced by Kodaira embedding converges to the first Chern form of the bundle. In this talk, we study an extension of this theorem by combining Kodaira embedding with Berezin-Toeplitz quantization. Moreover, if the manifold is compact, such a question is linked to the study of the smallest eigenvalues of Toeplitz operators associated with a given symbol, and recent results will be presented.