$\nu$SpaceSim is a comprehensive end-to-end simulation package created to facilitate the design of space-based and suborbital cosmic neutrino experiments that use the Earth as a neutrino converter as well as to understand the data obtained from current experiments. $\nu$SpaceSim models all aspects of the processes that lead to the neutrino-induced extensive air shower (EAS) signals: the modeling of neutrino interactions inside the Earth, propagating the leptons through the Earth into the atmosphere, modeling the tau-lepton decays, forming composite EAS, generating the air optical Cherenkov and radio signals, modeling their propagation and attenuation through the atmosphere. Finally, the response of optical and radio detectors is modeled. $\nu$SpaceSim uses a vectorized Python implementation to efficiently simulate neutrino-induced and background signals at a specific orbit or balloon altitude based on user xml input. The development has been focused on modeling the upward-moving EASs generated from Earth-emergent leptons sourced by neutrino interactions within the Earth, for both diffuse and transient sources accounting for the user-defined acceptance of an instrument. The tau-lepton channel is implemented using the modeling packages nuPyProp and nuLeptonSim. A MERRA-2 database driven application is used to generate cloud maps. Ionosphere dispersion of the radio signals is also modeled. In this paper, the $\nu$SpaceSim software, physics modeling, and the cosmic neutrino measurement capabilities of example experimental configurations will be presented.