Understanding the determinants of early introduction of sugar sweetened beverages (SSBs) may assist in designing effective public health interventions to prevent childhood weight related conditions (obesity). This study explores the relationship between family/infant characteristics and the early introduction of SSBs among infants in Sydney, Australia. Mothers (n = 934) from an ongoing birth cohort study were interviewed at 8, 17, 34, and 52 weeks postpartum. Multivariable logistic regression analysis was used to identify family/infant factors independently associated with the likelihood of early introduction of SSBs (<52 weeks of age). Of the 934 mothers interviewed, 42.7% (n = 399) of infants were introduced to SSBs before 52 weeks. Mothers who were born in Vietnam (adjusted Odds Ratio (AOR) = 2.14; 95% confidence interval (CI) 1.33, 3.47), other Asian countries (AOR = 1.62; 95% CI 1.02, 2.58) as well as single mothers (AOR = 3.72; 95% CI 2.46, 5.62) had higher odds of introducing SSBs early to their infants. Mothers from highly advantaged socioeconomic background (AOR = 0.43; 95% CI 0.28, 0.68), those who breastfed their baby for 17–25 weeks (AOR = 0.60; 95% CI 0.37, 0.99), 26–51 weeks (AOR = 0.65; 95% CI 0.45, 0.94), and 52 weeks or more (AOR = 0.62; 95% CI 0.43, 0.90); and those who introduced solids between 17–25 weeks (AOR = 0.58; 95% CI 0.36, 0.91) and 26 weeks or more (AOR = 0.55; 95% CI 0.34, 0.91) had reduced odds of introducing SSBs early. Tailoring health promotion programs for these vulnerable groups may delay the introduction of SSBs.