We study Glauber dynamics for the low temperature $(2+1)$D Solid-On-Solid model on a box of side-length $n$ with a floor at height $0$ (inducing entropic repulsion) and a competing bulk external field $λ$ pointing down (the prewetting problem). In 1996, Cesi and Martinelli showed that if the inverse-temperature $β$ is large enough, then along a decreasing sequence of critical points $(λ_c^{(k)})_{k=0}^{K_β}$ the dynamics is torpid: its inverse spectral gap is $O(1)$ when $λ\in (λ_c^{(k+1)},λ_c^{(k)})$ whereas it is $\exp[Θ(n)]$ at each $λ_c^{(k)}$ for each $k\leq K_β$, due to a coexistence of rigid phases at heights $k+1$ and $k$. Our focus is understanding (a) the onset of metastability as $λ_n\uparrowλ_c^{(k)}$; and (b) the effect of an unbounded number of layers, as we remove the restriction $k\le K_β$, and even allow for $λ_n\to 0$ towards the $λ= 0$ case which has $O(\log n)$ layers and was studied by Caputo et al. (2014). We show that for any $k$, possibly growing with $n$, the inverse gap is $\exp[\tildeΘ(1/|λ_n-λ_c^{(k)}|)]$ as $λ\uparrow λ_c^{(k)}$ up to distance $n^{-1+o(1)}$ from this critical point, due to a metastable layer at height $k$ on the way to forming the desired layer at height $k+1$. By taking $λ_n = n^{-α}$ (corresponding to $k_n\asymp \log n$), this also interpolates down to the behavior of the dynamics when $λ=0$. We complement this by extending the fast mixing to all $λ$ uniformly bounded away from $(λ_c^{(k)})_{k=0}^\infty$. Together, these results provide a sharp understanding of the predicted infinite sequence of dynamical phase transitions governed by the layering phenomenon.