Pure gauge theories in more than one spatial dimension are extremely interesting as they allow pure gauge observables such as glueballs and Wilson loops. Simulating the real-time dynamics of pure non-Abelian lattice gauge theories poses a significant computational challenge due to the large number of spurious gauge degrees of freedom. This work presents a brute-force (exact diagonalization) study of 2+1-dimensional SU(2) lattice gauge theory, leveraging the gauge-invariant Loop-String-Hadron (LSH) framework. Using only CPU-based computation, we have successfully demonstrated classical simulation on systems of up to 9 plaquettes and aim to push it further by leveraging combinations of CPUs and GPUs. This work provides crucial benchmarks for GPU implementations, near-term tensor network simulators, and quantum simulations, opening a new avenue for studying fundamental phenomena like thermalization in a non-Abelian gauge theory directly from the Hamiltonian perspective in higher dimensions.