Vibrational levels of the electronic ground states in dye molecules have not been previously explored at a high resolution in solid matrices. We present new spectroscopic measurements on single polycyclic aromatic molecules of dibenzoterrylene embedded in an organic crystal made of para-dichlorobenzene. To do this, we use narrow-band continuous-wave lasers and combine spectroscopy methods based on fluorescence excitation and stimulated emission depletion to assess individual vibrational linewidths in the electronic ground state at a resolution of ∼30MHz dictated by the linewidth of the electronic excited state. In this fashion, we identify several exceptionally narrow vibronic levels with linewidths down to values around 2GHz. Additionally, we sample the distribution of vibronic wavenumbers, relaxation rates, and Franck-Condon factors, in both the electronic ground and excited states for a handful of individual molecules. We discuss various noteworthy experimental findings and compare them with the outcome of density functional theory calculations. The highly detailed vibronic spectra obtained in our work pave the way for studying the nanoscopic local environment of single molecules. The approach also provides an improved understanding of the vibrational relaxation mechanisms in the electronic ground state, which may help create long-lived vibrational states for applications in quantum technology.