Short-period super-Earths and mini-Neptunes encircle more than ~50% of Sun-like stars and are relatively amenable to direct observational characterization. Despite this, environments in which these planets accrete are difficult to probe directly. Pairs of planets that are close to orbital resonances provide a unique window into the inner regions of protoplanetary disks, as they preserve the conditions of their formation and the early evolution of their orbital architectures. We present a novel approach toward quantifying transit timing variations within multi-planetary systems and examine the near-resonant dynamics of over 100 planet pairs detected by Kepler. Using an integrable model for first-order resonances, we find a clear transition from libration to circulation of the resonant angle at a period ratio of ~0.6% wide of exact resonance. The orbital properties of these systems indicate that they systematically lie far away from the resonant forced equilibrium. Cumulatively our modeling indicates that while orbital architectures shaped by strong disk damping or tidal dissipation are inconsistent with observations, a scenario with stochastic stirring by turbulent eddies in the protoplanetary disk reproduces several features of the data.