  We present the first quasi-exact \textit{ab initio} path integral Monte Carlo
(PIMC) results for the dynamic local field correction
$\widetilde{G}(\mathbf{q},z_l;r_s,\Theta)$ in the imaginary Matsubara frequency
domain, focusing on the strongly coupled finite temperature uniform electron
gas. These allow us to investigate the impact of dynamic exchange--correlation
effects onto the static structure factor. Our results provide a straightforward
explanation for previously reported spurious effects in the so-called
\textit{static approximation} [Dornheim \textit{et al.},
\textit{Phys.~Rev.~Lett.}~\textbf{125}, 235001 (2020)], where the
frequency-dependence of the local field correction is neglected. Our findings
hint at the intriguing possibility of constructing an analytical four-parameter
representation of $\widetilde{G}(\mathbf{q},z_l;r_s,\Theta)$ valid for a
substantial part of the phase diagram, which would constitute key input for
thermal density functional theory simulations.
