Background/Objectives: Biological products are emerging as therapeutic management options for intervertebral disc (IVD) degenerative affections and lower back pain. Autologous and allogeneic cell therapy protocols have been clinically implemented for IVD repair. Therein, several manufacturing process design considerations were shown to significantly influence clinical outcomes. The primary objective of this study was to preclinically qualify (chondrogenic potential, safety, resistance to hypoxic and inflammatory stimuli) cryopreserved primary progenitor cells (clinical grade FE002-Disc cells) as a potential cell source in IVD repair/regeneration. The secondary objective of this study was to assess the cell source’s delivery potential as cell spheroids (optimization of culture conditions, potential storage solutions). Methods/Results: Safety (soft agar transformation, β-galactosidase, telomerase activity) and functionality-related assays (hypoxic and inflammatory challenge) confirmed that the investigated cellular active substance was highly sustainable in defined cell banking workflows, despite possessing a finite in vitro lifespan. Functionality-related assays confirmed that the retained manufacturing process yielded strong collagen II and glycosaminoglycan (GAG) synthesis in the spheroids in 3-week chondrogenic induction. Then, the impacts of various process parameters (induction medium composition, hypoxic incubation, terminal spheroid lyophilization) were studied to gain insights on their criticality. Finally, an optimal set of technical specifications (use of 10 nM dexamethasone for chondrogenic induction, 2% O2 incubation of spheroids) was set forth, based on specific fine tuning of finished product critical functional attributes. Conclusions: Generally, this study qualified the considered FE002-Disc progenitor cell source for further preclinical investigation based on safety, quality, and functionality datasets. The novelty and significance of this study resided in the establishment of defined processes for preparing fresh, off-the-freezer, or off-the-shelf IVD spheroids using a preclinically qualified allogeneic human cell source. Overall, this study underscored the importance of using robust product components and optimal manufacturing process variants for maximization of finished cell-based formulation quality attributes.