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A linear Breit-Wheeler module for the code geant4 has been developed. This allows signal-to-noise ratio calculations of linear Breit-Wheeler detection experiments to be performed within a single framework. The interaction between two photon sources is modeled by treating one as a static field, then photons from the second source are sampled and tracked through the field. To increase the efficiency of the module, we have used a Gaussian process regression, which can lead to an increase in the calculation rate by a factor of up to 1000. To demonstrate the capabilities of this module, we use it to perform a parameter scan, modeling an experiment based on that recently reported by Kettle et al. [New J. Phys. 23, 115006 (2021)NJOPFM1367-263010.1088/1367-2630/ac3048]. We show that colliding 50-fs duration γ rays, produced through bremsstrahlung emission of a 100 pC, 2-GeV laser wakefield accelerator beam, with a 50-ps x-ray field, generated by a germanium burn-through foil heated to temperatures >150  eV, this experiment is capable of producing >1 Breit-Wheeler pair per shot.