The stage corresponding to effective droplet nucleation on the macroscopic condensation nuclei during the gradual creation of the metastable state in vapor was studied in a case when the diffusion growth of supercritical droplets prevails. The conditions of the applicability of the kinetic theory were analyzed. It was revealed that the macroscopicity of the condensation nuclei results in more severe conditions. The algorithm of the calculation of the all important kinetic characteristics of the droplet nucleation process, i.e., the total number of nucleating droplets, the time of the beginning of the droplet nucleation and the duration of this process, and the width of the droplet size spectrum, was formulated. It was shown that under the given properties of the vapor-gas medium and the liquid condensing from vapor, as well as at the given dimensions of the condensation nuclei, the algorithm allows us to cover the entire range of the characteristic times of the creation of the metastable state in vapor and the initial concentration of condensation nuclei admitted by the conditions of the applicability of the kinetic theory. Based on the algorithm, numerical calculations were performed demonstrating the ability of the proposed theory to make some interesting and practical predictions in a rather wide range of the values of the initial parameters. The factors were revealed, which determine the prevalence of the diffusion or free molecular absorption of vapor by the supercritical droplets at the stage corresponding to their effective nucleation at the given initial parameters of the theory. The ability to apply the theory to the case of polydisperse condensation nuclei was demonstrated.