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 strength $tilde{q}$ is increased, where $tilde{q}$ is defined as the ratio of the initial excitation energy per particle to the characteristic spin interaction energy. For a weak quench of $tilde{q}<1$, long-wavelength spin excitations are dominantly generated, leading to the formation of irregular spin domains. With increasing $tilde{q}$, the length scale of the initial spin excitations decreases, and we demonstrate that the long-wavelength instability is strongly suppressed for high $tilde{q}>2$. The observed crossover behavior is found to be consistent with the Bogoliubov description of the dynamic instability of the initial spinor condensate.
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