Egg white protein hydrolysate generated with pepsin was investigated for the presence of peptides with self-assembly and hydrogelation properties. Incubation of the hydrolysates for 16 h resulted in aggregates with significantly (p < 0.05) lower free amino nitrogen and sulfhydryl contents, and higher particle diameter and surface hydrophobicity compared to the hydrolysates. LC-MS/MS analysis of the aggregates resulted in identification of 429 ovalbumin-derived peptides, among which the top-six aggregation-prone peptides IFYCPIAIM, NIFYCPIAIM, VLVNAIVFKGL, YCPIAIMSA, MMYQIGLF, and VYSFSLASRL were predicted using AGGRESCAN by analysis of the aggregation “Hot Spots”. NIFYCPIAIM had the highest thioflavin T fluorescence intensity, particle diameter (5611.3 nm), and polydispersity index (1.0) after 24 h, suggesting the formation of β-sheet structures with heterogeneous particle size distribution. Transmission electron microscopy of MMYQIGLF, and VYSFSLASRL demonstrated the most favorable peptide self-assembly, based on the formation of densely packed, intertwined fibrils. Rheological studies confirmed the viscoelastic and mechanical properties of the hydrogels, with IFYCPIAIM, NIFYCPIAIM, VLVNAIVFKGL, and VYSFSLASRL forming elastic solid hydrogels (tan δ < 1), while YCPIAIMSA and MMYQIGLF formed viscous liquid-like hydrogels (tan δ > 1). The results provide valuable insight into the influence of peptide sequence on hydrogelation and self-assembly progression, and prospects of food peptides in biomaterial applications.