The numerical simulation of hypersonic flows remains a domain of primary importance to design flight vehicles and assess their aerodynamic and aerothermal loads. This challenging task requires robust and accurate numerical methods. Bearing this in mind, we describe a novel positivity-preserving cell-centered Finite Volume discretization of the multidimensional Euler equations which relies on the partition of the cell faces into subfaces impinging at nodes [G. Gallice et al. JCP, 2022]. The subface flux approximation is deduced from an approximate Riemann solver which depends not only on the mean values of the cells adjacent to the subface but also on the velocity of the node from which the subface emanates. The construction of this approximate Riemann solver relies on a specific structure of the intermediate fluxes which mimics the decomposition of the physical flux into an advection part plus a Lagrangian part. The projection of the nodal velocity onto the unit normal of the subface might be viewed as a parameter in the aforementioned Riemann solver. This implies that the resulting interface flux is not uniquely defined and thus the present Finite Volume method is not conservative in the classical sense. We then enforce conservation by making sure the subface fluxes around a node sum up to zero which fixes the value of the nodal velocity. Finally, the resulting first-order explicit time discretization is able to guarantee the positivity of mass density and specific internal energy while ensuring entropy stability provided an explicit time step condition is satisfied. The robustness and the accuracy of this novel FV scheme have been assessed through various numerical tests. We observe its insensitivity to the numerical pathologies that plague classical face-based Finite Volume formulation preserving contact discontinuity.