by unavoidable coherent leakage out of the target state, which imposes an inherent trade off between achievable steady-state state fidelity and stabilization rate. In this work we demonstrate a protocol that achieves trade off-free Bell state stabilization in a qutrit-qubit system realized on a circuit-QED platform. We accomplish this by creating a purely dissipative channel for population transfer into the target state, mediated by strong parametric interactions coupling the second-excited state of a superconducting transmon and the engineered bath resonator. Our scheme achieves a state preparation fidelity of 84% with a stabilization time constant of 339 ns, leading to the lowest error-time product reported in solid-state quantum information platforms to date.