  The estimation of the K\"all\'en-Lehmann spectral density from gauge
invariant lattice QCD two point correlation functions is proposed, and explored
via an appropriate inversion method. As proof of concept the SU(2) glueball
spectrum for the quantum numbers $J^{PC} = 0^{++}$ is investigated for various
values of the lattice spacing. The spectral density and the glueball spectrum
are estimated using the published data of arXiv:1910.07756. Our estimates for
the ground state mass are in good agreement with the traditional approach
published therein, which is based on the large time exponential behaviour of
the correlation functions. Furthermore, the spectral density also contains
hints of excites states in the spectrum and, despite using non-optimized gauge
configurations, the method is able to estimate their mass values.
