This work aims to estimate material properties at a mesoscopic level using the PuMA Software from an uncertainty quantification perspective. The stochastic behavior of PuMA, mainly related to the random distribution of the fibers, is an intrinsic source of uncertainty. The choice of some physical parameters, such as the fiber’s thermal conductivity, is an additional source of uncertainties. The first contribution is a low-cost surrogate-based methodology with an unequal allocation scheme applied for the first time to the stochastic mesoscale characterization of ablative materials. A second contribution of this work is the uncertainty propagation and sensitivity analysis of the material properties, which also yields a systematic assessment of the choice of the voxel resolution for both the fibers and the domain. Precisely, the convergence of the quantities of interest can be surveyed, thus identifying the minimal reference elementary volume.