  Hybrid quantum photonics combines classical photonics with quantum emitters
in a postprocessing step. It facilitates to link ideal quantum light sources to
optimized photonic platforms. Optical cavities enable to harness the
Purcell-effect boosting the device efficiency. Here, we postprocess a
free-standing, crossed-waveguide photonic crystal cavity based on Si$_3$N$_4$
with SiV$^-$ center in nanodiamonds. We develop a routine that holds the
capability to optimize all degrees of freedom of the evanescent coupling term
utilizing AFM nanomanipulation. After a few optimization cycles we resolve the
fine-structure of individual SiV$^-$ centers and achieve a Purcell enhancement
of more than 4 on individual optical transitions, meaning that four out of five
spontaneously emitted photons are channeled into the photonic device. Our work
opens up new avenues to construct efficient quantum photonic devices.
