We search for emergent hydrodynamic modes in real-time Hamiltonian dynamics of 2+1-dimensional SU(2) lattice gauge theory on a quasi one dimensional plaquette chain, by numerically computing symmetric correlation functions of energy densities on lattice sizes of about 20 with the local Hilbert space truncated at j_max=1/2 Due to the Umklapp processes, we only find a mode for energy diffusion. The symmetric correlator exhibits transport peak near zero frequency with a width proportional to momentum squared at small momentum, when the system is fully quantum ergodic, as indicated by the eigenenergy level statistics. This transport peak leads to a power-law t^(-1/2) decay of the symmetric correlator at late time, also known as the long-time tail, as well as diffusion-like spreading in position space. We also introduce a quantum algorithm for computing the symmetric correlator on a quantum computer and find it gives results consistent with exact diagonalization when tested on the IBM emulator. Finally we discuss the future prospect of searching for the sound modes.