One key issue in the coronavirus disease 2019 (COVID-19) pandemic concerns understanding the impact of the vaccination program and non-pharmaceutical interventions (NPIs) in cases and deaths. The lack of comprehension of the vaccination program and NPIs strategies compromises their effectiveness in the future. Thus, this work aims to estimate the avoidable COVID-19 cases and deaths with the anticipation of vaccination, additional doses, and effective NPIs in Brazil. To this end, an experimental study applying a susceptible-exposed-infectious-recovered-susceptible model with parameters adjusted in a timeline using historical records from the Brazilian Unified Health of the Brazilian states estimates the number of cases and deaths for different vaccination program and NPIs scenarios in Brazil (from 2020 March 8 until 2022 June 5). The model-based estimate shows that 1.3 months of vaccination anticipation, additional vaccine doses, and a higher level the NPIs would reduce and delay the pandemic peak. There would be 17,121,749 fewer COVID-19 cases and 391,647 avoidable deaths in the country. Finally, our results suggest that if 80% of the Brazilian population had been vaccinated by May 2021, there would 59.83% of death avoided in Brazil.