  Within optical quantum information processing, single-photon sources based on
a two-level system in a semiconductor material allow for on-demand generation
of single photons. To initiate the spontaneous emission process, it is
necessary to efficiently populate the excited state. However, reconciling the
requirement for on-demand excitation with both high efficiency and high photon
indistinguishability remains a challenge due to the presence of charge noise
and phonon-induced decoherence in the solid-state environment. Here, we propose
a method for reconstructing the phonon spectral density experienced by
WSe$_{2}$ quantum emitters in the emission process. Using the reconstructed
phonon spectral density, we analyze the performance of the resonant,
phonon-assisted, and Swing-UP of the quantum EmitteR population (SUPER)
swing-up excitation schemes. Under resonant excitation, we obtain an exciton
preparation fidelity limited to $\sim$0.80 by the strong phonon coupling, which
improves to 0.96 for the SUPER scheme (or 0.89, depending on the type of
emitter considered). Under near-resonant phonon-assisted excitation, we observe
near-unity excitation fidelity up to 0.976 (0.997). Additionally, we
demonstrate that, assuming the suppression of the phonon sidebands, residual
dephasing mechanisms such as charge/spin fluctuations are the dominating
decoherence mechanisms undermining the photon indistinguishability.
