Discoveries of Frank-Kasper phases and closely related dodecagonal quasicrystals (DDQCs) in soft, mesoscopic systems have galvanized efforts to unveil the fundamental mechanisms that drive the formation of these remarkably complex micellar packings. Toward this end, we report temperature-dependent small-angle X-ray scattering analyses of a crystalline-amorphous poly(ethylene oxide)-block-poly(2-ethyl hexylacrylate) (OA) diblock copolymer with M-n = 8300 g/mol, D = M-w/ M-n = 1.10, and volume composition f (O) = 0.21. On heating at ambient temperature, this polymer assembles sequentially into five distinct morphologies prior to melt disordering at T-ODT = 69 degrees C: semicrystalline lamellae (L-c), a liquid-like packing (LLP) of particles lacking translational order, an aperiodically ordered DDQC, a periodic FK sigma phase, and a body-centered cubic (BCC) packing of particles. Detailed investigations of thermal processing conditions that foster DDQC formation reveal that this metastable morphology only forms in melts exhibiting LLP characteristics arising from either melting the Lc phase at low temperature or quenching a high-temperature disordered state, and that this DDQC eventually evolves into a sigma approximant phase. Cooling a well-ordered BCC phase induces direct formation of a sigma phase with no evidence of DDQC formation, suggesting the critical importance of particle size distribution of the disorganized yet segregated LLP state in triggering the emergence of a DDQC.