With nearly 11 billion doses of the COVID-19 vaccine being administered, stark differences in the vaccination rates persist. Vaccine distribution initiatives such as COVAX and African Vaccine Acquisition Trust (AVAT) were formed to ensure equitable vaccine delivery. This review evaluates the initial COVID-19 vaccination efforts and the impact of different vaccine distribution initiatives on equitable vaccination coverage in the early phase. We conducted a descriptive and trend analysis with sub-groups by various context parameters of data on COVID-19 vaccination from December 2020 till February 2022, from four public databases including UNICEF, WHO, COVID-19 Task Force and Our World in Data to examine COVID-19 vaccine distribution progress and the contributions of vaccine procurement initiatives. We found that High Income Countries (HICs) had much higher vaccination rate (78.4%) than Lower-Middle-Income Countries (LMICs) (55.5%) and Low-Income Countries (LICs) (10.9%). Large differentials (>80% to <10%) in the vaccination rates of eligible population of adults in LMICs and LICs existed. Differentials in the total vaccine doses delivered to each country ranged from 355.6% to 4.8% of the total population. In LICs, 53.3% of the total doses were obtained via COVAX, 30.9% by bilateral/multilateral agreements, 6.5% by donations and 3.8% by AVAT. In LMICs, 56.4% of total vaccines procured were via bilateral/multilateral agreements, 21.4% by COVAX, 4.2% by donations and 0.5% by AVAT. COVAX delivered 1 billion doses by January 2022 which constituted 53.2% and 21.4% of procured doses in LICs and LMICs. In LICs and LMICs, 6.5% and 4.2% of total doses were acquired through donations while 30.9% and 56.4% of doses were purchased. Despite global efforts, significant disparities were present in COVID-19 vaccination efforts amongst countries of different income groups. Future efforts should focus on addressing vaccine inequities explicitly and in improving global vaccine distribution.