While recent efforts have shown how local structure plays an essential role in the dynamic heterogeneity of homogeneous glass-forming materials, systems containing interfaces such as thin films or composite materials remain poorly understood. It is known that interfaces perturb the molecular packing nearby, however, numerous studies show the dynamics are modified over a much larger range. Here, we examine the dynamics in polymer nanocomposites (PNCs) using a combination of simulations and experiments and quantitatively separate the role of polymer packing from other effects on the dynamics, as a function of distance from the nanoparticle surfaces. After showing good qualitative agreement between the simulations and experiments in glassy structure and creep compliance, we use a machine-learned structure indicator, softness, to decompose polymer dynamics in our simulated PNCs into structure-dependent and structure-independent processes. With this decomposition, the free energy barrier for polymer rearrangement can be described as a combination of packing-dependent and packing-independent barriers. We find both barriers are higher near nanoparticles and decrease with applied stress, quantitatively demonstrating that the slow interfacial dynamics is not solely due to polymer packing differences, but also the change of structure–dynamics relationships. Finally, we present how this decomposition can be used to accurately predict strain-time creep curves for PNCs from their static configuration, providing additional insights into the effects of polymer–nanoparticle interfaces on creep suppression in PNCs.