Linear global non-modal instability analysis of the boundary layer over the Hypersonic International Flight Research Experimentation 5 (HIFiRE-5) rounded-tip 2:1 elliptic cone model is performed on a plane normal to the cone symmetry axis. The base flow has been computed using the US3D solver at Ma=7 and flight altitude of 33km and has been analyzed with respect to its modal instability in earlier work. The present objective is to interrogate the same flow regarding the existence of optimal transiently growing small-amplitude disturbances and correlate the latter with exponentially-growing modal instability mechanisms that have been confirmed to exist in this flow. Perturbation energy growth is calculated here using Singular Value Decomposition (SVD) of the linearized Navies-Stokes evolution operator: local transient growth analysis is performed by linearizing about an one-dimensional profile extracted from the base flow, while global non-modal analysis is performed by performing the SVD of the operator linearized about the full two-dimensional steady state on the plane. In both cases linear optimal perturbations are computed; local results are consistent with those of earlier analysis of the compressible flat-plate boundary layer, while global transient growth analysis results obtained herein reveal both symmetric and antisymmetric global modes emerging out of the temporal integration of the linearized operator in the limit of asymptotically large times. This scenario of emergence of modal perturbations in a non-modal analysis, in which no explicit assumption of harmonic time-dependence of linear perturbations has been made, is consistent with analogous findings in a number of incompressible flows and reconciles earlier modal and non-modal linear instability analysis results obtained on the HIFiRE-5 model configuration.