Background: The World Health Organization (WHO) recommends early initiation of breastfeeding (EIBF) within the first hour after birth. However, certain perinatal factors, namely caesarean section, may prevent this goal from being achieved. The aim of our study was to examine the relationship between EIBF (maternal lactation in the first hours and degree of latching before hospital discharge) and the maintenance of exclusive breastfeeding (MBF) up to the recommended 6 months of age (as advocated by the WHO). Methods: This observational, retrospective cohort study included a random sample of all births between 2018 and 2019, characterising the moment of breastfeeding initiation after birth and the infant’s level of breast latch (measured by LATCH assessment tool) prior to hospital discharge. Data were collected from electronic medical records and from follow-up health checks of infants up to 6 months postpartum. Results: We included 342 women and their newborns. EIBF occurred most often after vaginal (p < 0.001) and spontaneous births with spontaneous amniorrhexis (p = 0.002). LATCH score <9 points was associated with a 1.4-fold relative risk of abandoning MBF (95%CI: 1.2–1.7) compared with a score of 9–10 points. Conclusions: Although we were unable to find a significant association between EIBF in the first 2 h after birth and MBF at 6 months postpartum, low LATCH scores prior to discharge were associated with low MBF, indicating the importance of reinforcing the education and preparation efforts of mothers in the first days after delivery, prior to the establishment of an infant feeding routine upon returning home.