The regularities of non-stationary diffusion growth of overcritical gas bubbles and kinetics of their distribution in sizes in a supersaturated-by-gas liquid solution on the nucleation stage have been analytically described by taking into account the full-scale influence of viscous and capillary forces on pressure in the overcritical bubbles. The results are general and not limited by values of gas supersaturation and gas solubility in the surrounding liquid solution. It is shown how the nonuniform concentration profile of the dissolved gas in supersaturated solution around the growing bubble changes with time and distance from the center of the overcritical bubble and gradually transforms into a stationary (at low solubility and moderate supersaturation of the dissolved gas) or self-similar profile (at large solubility and supersaturation of the dissolved gas). The kinetic theory of the nucleation stage with the excluded volume has been extended to the case of non-stationary gas concentration profiles due to viscous and capillary forces. The general approach has been illustrated in the limiting case of negligible viscous but significant capillary contributions to the vapor pressure in the bubble and in the case when the approximation of the mean field of gas supersaturation can be applied.