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In this article we investigate the temporal regularity of strong solutions tothe stochastic $p$-\com{L}aplace system in the degenerate setting, $p \in[2,\infty)$, driven by a multiplicative nonlinear stochastic forcing. Weestablish $1/2$ time differentiability in an expontential Besov-Orlicz spacefor the solution process $u$. Furthermore, we prove $1/2$ timedifferentiability of the nonlinear gradient $|\nabla u|^{\frac{p-2}{2}} \nablau$ in a Nikolskii space.

On temporal regularity for strong solutions to stochastic $p$-Laplace systems