When spin ice systems undergo a sudden thermal quench, they have been shown to enter long-lived metastable states where the monopole excitations form so-called noncontractible pairs [Phys. Rev. Lett. 104, 107201 (2010)]. While the nature of these states is well understood, the dynamical mechanisms underpinning their formation remain largely unexplored and are the subject of this study. We find that the long-range tail of the Coulomb interactions between monopoles plays a central role by suppressing the monopole-assisted decay of noncontractible pairs with respect to monopole-antimonopole annihilation. In conjunction with low final quench temperatures, where the system enters a nonhydrodynamic regime in which the monopoles effectively move at terminal velocity in the direction of the local force acting on them, the interactions lead to a metastable plateau that persists in the thermodynamic limit. This is a remarkable phenomenon, reminiscent of jamming and some instances of glassiness: A transient modification of the short-time dynamics of the system allows it to enter a metastable state whose lifetime can easily be astronomically large at (experimentally relevant) low temperatures. We demonstrate this using Monte Carlo simulations and mean field population dynamics theory, and we provide an analytical understanding of the mechanisms at play. When the interactions between monopoles are truncated to finite range, the metastable plateau reduces to a finite size effect. We derive the finite size scaling behaviour of the density of noncontractible pairs in the metastable plateau for both short- and long-range interactions, and discuss the experimental implications of our results.