Formation of a dendritic grain starts from nucleation and then growth propagation occurs. Through the in situ and real-time solidification experiments of Al-Cu alloys observed by synchrotron X-ray imaging, it is found that the early-stage free growth rate of dendritic grains goes far beyond the concept described by the classical crystal growth theory. The rate gradually drops down even though the liquid is continuously cooled down. Quantitative 3D phase-field simulations demonstrate that this abnormal early-stage growth behavior depends strongly on the nucleation. A critical nucleus can grow rapidly to a peak rate driven by the initial nucleation undercooling, and then its rate gradually drops down to a minimum before it approaches the steadystate free growth regime. This strong dependence of the early-stage growth on the nucleation is then supported by an analytical model, and this correlation enables the accurate identification of the nucleation undercooling for each grain in the experiment and thus allows for a large-scale quantitative simulation of the real-time observed polycrystalline growth. This progress provides a comprehensive understanding on the crystal growth kinetics from a critical nucleus to the growth end, and thus will provide a new theoretical framework to design novel technology to control the solidification microstructures.