We investigate the early-time dynamics of a quasi-two-dimensional spin-1 antiferromagnetic Bose-Einstein condensate after a sudden quench from the easy-plane to the easy-axis polar phase. The post-quench dynamics shows a crossover behavior as the quench strengthq is increased, whereq is defined as the ratio of the initial excitation energy per particle to the characteristic spin interaction energy. For a weak quench, long-wavelength spin excitations are dominantly generated, leading to the formation of irregular spin domains. With increasingq, the length scale of the initial spin excitations decreases, and we demonstrate that the long-wavelength instability is strongly suppressed for a high value ofq > 2. The observed crossover behavior is found to be consistent with the Bogoliubov description of the dynamic instability of the initial spinor condensate.