The Froissart–Martin bound has long provided the only universal constraint on the high-energy growth of total cross-sections, but its asymptotic nature has limited its use at collider energies. We use the nonperturbative S-matrix bootstrap to derive a universal finite-energy bound on an averaged total cross-section. The bound reproduces Froissart growth at high energy and determines subleading corrections: the leading correction is universal, while the first theory-dependent term is controlled by low-energy S-matrix data that can itself be bounded by the bootstrap. Comparing the finite-energy bound with proton–proton data shows that TeV-scale scattering remains far from the asymptotic Froissart regime. The extremal bootstrap amplitude further displays qualitative signatures of soft hadronic scattering, including a rising total cross-section, diffractive-cone shrinkage, diffractive minima, and towers of higher-spin resonances. Our results provide a finite-energy, first-principles framework for forward hadronic scattering.