Low-income countries (LICs) and lower-middle-income countries (LMICs) are still deprived of the optimum doses of coronavirus disease 2019 (COVID-19) vaccines for their population, equal access and distribution, as well as mass immunization roadmaps to be implemented for achieving herd immunity and protection from the ongoing pandemic. In this short report, we are interacting with the world public health experts, as well as national and global leaders for warranting the mass vaccination drive to be more progressive against COVID-19 with equitable access of vaccines to LICs or LMICs to save the lives of the poorest country people and refugees. From several scientific databases, such as Google Scholar, PubMed, as well as national and international news websites, the data were collected data by utilizing appropriate keywords regarding the topic. Bangladesh might be exemplified in this brief communication as the representative of LMIC. As of October 14, 2021, 48% of the world's people have received at least one dose of the COVID-19 vaccine. In contrast, only 2.5% of people from LICs have come in under COVID-19 vaccination for at least a single shot. Both LICs and LMICs need far more vision and ambition, including political, administrative, and diplomatic progress along with enhancing the vaccination drive for their population to be immunized through simultaneous mass vaccination progress of other countries with implementing public health safety measures against the COVID-19 pandemic.