This paper develops a numerical model of cosmic-ray interactions with the Earth's atmosphere using the Geant4 Monte Carlo package, and simulates the neutron flux distribution over flat, unshielded terrain at various latitudes and altitudes globally. The production rates of cosmogenic nuclides (¹⁰Be, ²⁶Al, ¹⁴C, and ²¹Ne) are calculated using a "baseline production rate + flux scaling factor" strategy: baseline production rates for each nuclide are first obtained by convolving the neutron energy spectrum with experimental excitation functions at a reference point, and then extrapolated globally using the spatial scaling factors of neutron flux derived from Geant4 simulations. The results are systematically compared with the Argento (MCNP) and Lifton (LSDn) models, showing good agreement under most conditions. This work is based on a pure Geant4 framework, with all scaling factors derived from unified physical simulations and without introducing any empirical scaling factors fitted to measured data. It provides a physically self-consistent baseline reference for global-scale calculations of cosmogenic nuclide production rates.