Well-dispersed, solvent-free silica nanoparticles tethered with polymers exhibit soft glassy rheology and jamming behavior due to “cages” induced by interpenetrated chains. In this study, we use small-angle X-ray scattering (SAXS) and rheology to investigate slow structural and mechanical evolution of a soft glassy material composed of silica nanoparticles densely grafted with poly(ethylene glycol) methyl ether (mPEG) chains. The measurements reveal significant equilibration processes in the materials that have not been reported previously, but appear characteristic of caging and of the soft-but-jammed state of matter in which the materials fall. Equilibration dynamics are found to be thermally activated and associated with local rearrangements of tethered chains to their equilibrium conformations. At fixed temperature, the strength of the equilibrated cages is inferred from the shear modulus at intermediate frequency and are observed to be substantially larger than the unequilibrated values, but to decrease in a predictable manner as temperature rises. We identify geometric confinement due to packing of spherical nanoparticles as the driving force for chain interpenetration, and propose a simple geometric model to rationalize equilibration processes in the materials in terms of corona interpenetration, cage dynamics, and yielding of self-suspended hairy nanoparticles. We further explore the effects of geometric confinement on caging behavior by dispersing the SiO2-PEG hairy nanoparticles in PEG oligomers. Jamming behavior analogous to the solvent-free systems is observed down to a critical core volume fraction of 0.065, substantially below where the glass-to-liquid transition is reported in suspensions of non-Brownian spheres. At particle concentrations above this value, the oligomer-suspended hairy nanoparticle systems exhibit a non-monotonic flow curve indicative of permanent shear banding below a critical shear rate. The stress decomposition shows a significant unrelaxable stress upon flow cessation, which likely corresponds to the chain orientations due to interpenetration. Spectroscopic analysis suggests that tethered chains adopt more trans conformations compared to untethered counterparts, providing molecular evidence of geometric confinement-induced chain interpenetration in hairy nanoparticle soft glasses.