The article deals with the problem of an initial state of quantum inflationary Universe. Considering the dynamics of the inflation scalar field at the beginning of the inflation stage in the context of semi-classical approximation, we have identified this field with a cosmic time parameter. The early Universe state was defined as an initial value of the inflation field. Other degrees of the Universe freedom, including the scale factor, are treated within the scope of the quantum theory. Then, the initial state of quantum degrees of freedom at the beginning of the inflation must be defined, as well. A principle of the least excitation of physical degrees of freedom for the Universe has been proposed to determine the initial state of the quantum universe. A uniform anisotropic model of the Universe was considered where its size and the anisotropic parameters were quantum dynamical variables. On the assumption that the Universe size is a radial variable in the configuration space of the theory the definition of the Hamiltonian of the Universe is rendered more precise. A simple exponential form of the Universe initial state is suggested and the Universe initial size being estimated for this form.