We present AC and DC magnetometry, heat capacity, muon spin relaxation ($mu$SR) and resonant inelastic X-ray scattering (RIXS) studies of the pyrochlore osmate Y$_2$Os$_2$O$_7$. We observe a non-zero effective moment governed by $sqrt{f}mu_{rm{eff}} = 0.417(1),mu_{rm{B}}$ where $f$ is the fraction of Os sites which exhibit a spin, and spin freezing at temperature $T_{rm f} simeq 5,$K, consistent with previous results. The field dependence of magnetisation data shows that the paramagnetic moment is most likely due to large moments $mu_{rm eff} simeq 3,mu_{rm B}$ on only a small fraction $f simeq 0.02$ of Os sites. Comparison of single-ion energy level calculations with the RIXS data yields a non-magnetic $J_{rm eff} = 0$ ground state on the Os$^{4+}$ sites. The spin-orbit interaction, Hunds coupling and trigonal distortion of OsO$_{6}$ octahedra are all important in modelling the experimentally observed spectra. We are able to rule out impurity effects, leaving disorder-related effects such as oxygen non-stoichiometry or site interchange between Os and Y ions as the most plausible explanation for the magnetic response in this material.
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