A quantum mechanical simulation of the initial stage of Si growth at CrSi₂(0001) has been performed. Growth was carried out by batch application of loose (0.3 ML portions) or dense (1 ML portions) Si atomic condensate to the surface of CrSi₂(0001) frozen at 0 K, followed by its relaxation under the influence of quantum mechanical forces. It is shown that in the first case, Si surface phases are formed, consisting of an array of 2D and then 3D Si clusters with a tetrahedral sp³ bond. And in the second case, the formation of a solid-phase wetting layer (TSS) Si occurs: first in the form of a pseudomorphic, and then a less stable polymorphic (packing) layer. The pseudomorphic solid-phase wetting layer, in this case, repeats the three-layer packing (ABC) of atoms in the CrSi₂(0001) substrate, and the polymorphic solid-phase wetting layer, in addition to packing ABC, additionally acquires a two-layer packing of AB atoms. It has been found that, at least at 1-3 ML of Si, a density spectrum of electronic states characteristic of a metal is formed in a solid-phase Si wetting layer on CrSi₂(0001). Keywords: two-dimensional phases, solid-phase wetting layers, atom packing, phase transition, quantum mechanical modeling, Si, CrSi₂(0001).