High fidelity simulations such as Large Eddy Simulations (LES) are commonly used in combustion research. While turbulence and combustion models become increasingly precise, these simulations still rely on kinetic mechanisms that carry uncertainties that may significantly impact the flame's quantities of interest. In this study, we focus on the lift-off height of the H2 Cabra flame, which is largely affected by the uncertainty of the operating conditions specifically by the uncertainty of the co-flow temperature. To properly compare experimental and numerical results, one must account for both experimental and numerical uncertainties. A 32-dimensional uncertain space is determined, one dimension corresponding to the co-flow temperature and the others from the uncertain kinetic mechanism. This high-dimensionality means that direct Monte-Carlo or surrogate-based approaches are intractable. A representative physical model of reduced computational cost is used to conduct a global sensitivity analysis. From this, a two-dimensional uncertain space is uncovered, in which most of the variance of the quantity of interest is retrieved, allowing a future uncertainty propagation study in LES of the H2 Cabra flame.