In Senegal, studies focusing specifically on vaccination coverage with the Bacille de Calmette et Guérin (BCG) vaccine, the birth dose of oral polio vaccine (OPV zero dose) and the birth dose of hepatitis B (HepB-BD) vaccine are insufficient. This study aimed to highlight vaccination coverages with birth doses and factors associated with timely vaccination in Podor health district. Methods A cross-sectional study was carried out from June 19 to 22, 2020. The study population consisted of children aged 12 to 23 months of which 832 were included. A stratified two-stage cluster survey was carried out. The sources of data were home-based records (HBR), health facility registries (HFR) and parental recalls. Timely vaccination refers to any vaccination that has taken place within 24 h after birth. Descriptive analyzes, the chi-square test and logistic regression were performed. Results The crude vaccination coverages with BCG, OPV zero dose and HepB-BD were 95.2%, 88.3% and 88.1%, respectively. Vaccination coverages within 24 h after birth were estimated at 13.9%, 30% and 42.1%, respectively. The factors associated with timely HepB-BD are delivery in a health facility (AOR = 1.55; 95% CI = 1.02–2.40), access to television (AOR = 1.63; 95% CI = 1.16–2.29), weighing (AOR = 3.92; 95% CI = 1.97–8.53) and hospitalization of the newborn immediately after birth (AOR = 0.42; 95% CI = 0.28–0.62). Conclusion Timely administration of birth doses is a challenge in the Podor health district. The solutions would be improving geographic access to health facilities, involving community health workers, raising awareness and integrating health services.