For models with high-dimensional input spaces, constructing accurate response surfaces can be prohibitively expensive. Additionally, the high-dimensionality of the parameter spaces can impact the computational cost of a parameter investigation. Using an active subspace construction, we can efficiently approximate complex models by constructing low-order response surfaces based on a smaller subspace of the high-dimensional parameter space. We employ a gradient-free active subspace construction for dimension reduction of the input space. In this talk, I will introduce an initialization algorithm for the gradient-free method that addresses cases where the input dimension renders the gradient-free method infeasible.