With a community-centric approach to achieve Sustainable Development Goal 6.1, the Jal Jeevan Mission (JJM) launched in 2019, aims to improve the living standard of rural communities by addressing various issues related to rural drinking water supply system. The literature evaluating rural water supply programs in India is sparse. Emphasizing the large-scale implementation of the mission, we utilized sample survey data and multiple linear regression models to investigate whether or not access to household water tap connections has succeeded in reducing the burden of drinking water collection on women and female children in rural regions. Overall, our findings suggest moderate attainment of JJM even at a very early stage, whereas the positive achievements are reflected in terms of reducing the burden of water collection on women. Further, a higher probability of wealth-related inequity favoring advantaged groups was found in the coverage of household water tap connections both in pre- and initial-JJM period. Our study suggests ground-level strengthening of the rural drinking water supply system for achieving an equitable and sustainable outreach of the program across the country.