  Fast and high-fidelity qubit initialization is crucial for low-frequency
qubits such as fluxonium, and in applications of many quantum algorithms and
quantum error correction codes. In a circuit quantum electrodynamics system,
the initialization is typically achieved by transferring the state between the
qubit and a short-lived cavity through microwave driving, also known as the
sideband cooling process in atomic system. Constrained by the selection rules
from the parity symmetry of the wavefunctions, the sideband transitions are
only enabled by multi-photon processes which requires multi-tone or strong
driving. Leveraging the flux-tunability of fluxonium, we circumvent this
limitation by breaking flux symmetry to enable an interaction between a
non-computational qubit transition and the cavity excitation. With single-tone
sideband driving, we realize qubit initialization with a fidelity exceeding 99%
within a duration of 300 ns, robust against the variation of control
parameters. Furthermore, we show that our initialization scheme has a built-in
benefit in simultaneously removing the second-excited state population of the
qubit, and can be easily incorporated into a large-scale fluxonium processor.
