Dynamic earthquake source inversions aim to determine the spatial distribution of initial stress and friction parameters leading to dynamic rupture models that reproduce observed ground motion data. Such inversions are challenging, particularly due to their high computational burden; thus, so far, only few attempts have been made. Using a highly efficient rupture simulation code, we introduce a novel method to generate a representative sample of acceptable dynamic models from which dynamic source parameters and their uncertainties can be assessed. The method assumes a linear slip-weakening friction law and spatially variable prestress, strength, and characteristic slip-weakening distance along the fault. The inverse problem is formulated in a Bayesian framework, and the posterior probability density function is sampled using the Parallel Tempering Monte Carlo algorithm. The forward solver combines a 3-D finite difference code for dynamic rupture simulation on a simplified geometry to compute slip rates and precalculated Green's functions to compute ground motions. We demonstrate the performance of the proposed method on a community benchmark test for source inversion. We find that the dynamic parameters are resolved well within the uncertainty, especially in areas of large slip. The overall relative uncertainty of the dynamic parameters is rather large, reaching ~50% of the averaged values. In contrast, the kinematic rupture parameters (rupture times, rise times, and slip values), also well resolved, have relatively lower uncertainties of ~10%. We conclude that incorporating physics-based constraints, such as an adequate friction law, may serve also as an effective constraint on the rupture kinematics in finite-fault inversions.