We calculate the real-time symmetric correlation function of the stress-energy tensor for a near-integrable Ising field theory consisting of three stable scalar particles via lattice Hamiltonian simulation. Using classical exact diagonalization and the matrix product state tensor network methods, we find that in the scaling region of the lattice theory, Umklapp processes that break continuum momentum conservation are suppressed and the sound modes of relativistic hydrodynamics emerge at long wavelength and late time in non-equilibrium dynamics. The extracted ratio of bulk viscosity to entropy density is $\zeta /s=3.06\pm 0.68$ and the speed of sound is $c_s/c=0.76\pm 0.02$ at the temperature $T\approx 7.14$ in units of the lowest stable particle’s mass. Our study demonstrates the utility of real-time lattice Hamiltonian simulation for describing hydrodynamization and calculating transport coefficients nonperturbatively.