Background/Objectives: Cesarean delivery often leads to delayed breastfeeding initiation, potentially affecting infant health compared with vaginal delivery. This prospective observational study (conducted between August 2022 and January 2024) comparatively evaluates the impact of delivery method—vaginal, planned cesarean, and emergency cesarean—on breastfeeding initiation and continuation and examines the maternal factors influencing these outcomes. Materials and Methods: We enrolled 338 mother–infant pairs at a tertiary university hospital. Breastfeeding effectiveness was assessed using the Bristol Breastfeeding Assessment Tool (BBAT) at birth and at one, three, and six months postpartum. Rates of breastfeeding continuation and formula supplementation were documented through structured interviews. Results: The mothers who delivered vaginally had a significantly higher rate of breastfeeding within one hour after birth (85.5%) compared with planned (57.9%) and emergency cesarean sections (64.9%) (p < 0.001). Baseline BBAT scores were higher for vaginal births but converged across the groups by one month postpartum (p > 0.05). At six months, breastfeeding continuation rates remained high (94.4–95.2%) irrespective of delivery method. Conclusions: Delivery method exerts a transient effect on breastfeeding initiation. With lactation support, the mothers delivering by cesarean section achieved comparable breastfeeding outcomes within the first month postpartum. These findings reinforce the importance of Baby-Friendly Hospital Initiative (BFHI) practices, including immediate skin-to-skin contact, effective pain management, and lactation counseling, in ensuring equitable breastfeeding outcomes.