A key problem within single-photon sources engineering is to achieve population inversion of a quantum emitter on-demand and with the highest possible fidelity, without resorting to resonant laser pulses. A non-resonant pumping signal has the advantage of being separated in frequency from the single photons, but it typically triggers -or makes active use of -incoherent phonon-assisted scattering events, which preclude near unity fidelity in the population inversion and deteriorate the quality of the emitted photons. Here, we theoretically show that a coherent di-chromatic pumping scheme using short laser pulses and moderately large detuning effectively decouples the emitter from its phonon bath, allowing for population inversion arbitrarily close to unity. When considering a micropillar single-photon source driven with this scheme, we calculate very high photon emission into the cavity mode (0.953 photons per pulse), together with excellent indistinguishability (0.975). Such values are uniquely bounded by decoherence in the emission dynamics or practical considerations, and not by the excitation scheme.