The rise of digital twins has enabled deeper exploration on how to use modeling and simulation earlier and continuously throughout the design and acquisition process. For models to be called upon more frequently and throughout this process, it is necessary that their outputs are reliable and trustworthy. A standard practice in modeling and simulation is to have models undergo a verification, validation, and uncertainty quantification (VVUQ) procedure. The scope of this work is to assemble and demonstrate a UQ framework for digital twin applications, with the case study having a focus on material development and design through a mesoscale model of a three-dimensional carbon/carbon composite. This framework allows for microscale uncertainties to propagate to the mesoscale, providing a multi-scale model to determine the effective macroscale material properties. Our framework will compare traditional approaches, such as Monte Carlo Methods, known for large sampling sizes and high computational cost to a surrogate model using Polynomial Chaos Expansion (PCE), which requires significantly less samples and has a significantly lower computational cost. For this application, the chosen stochastic parameters that are being varied are: tow spacing, tow waviness, and porosity. All of these parameters rely on manufacturing-related uncertainties. To demonstrate a trustworthy model, verification will be performed via the method of manufactured solutions with mesh refinement through a representative volume element (RVE), where convergence of the numerical method will also be recovered. Validation will be achieved by comparing results to published data on carbon/carbon composite effective material properties. The results are presented as probability distribution functions (PDF) for the effective macroscale material properties of the composite. The framework demonstrates the capabilities of using both Monte Carlo Methods and PCE as effective methods to propagate uncertainty in a subsystem of models.