Policymakers in developing countries increasingly see science, technology, and innovation (STI) as an avenue for meeting sustainable development goals (SDGs), with STI-based startups as a key part of these efforts. Market failures call for government interventions in supporting STI for SDGs and publicly-funded incubators can potentially fulfil this role. Using the specific case of India, we examine how publicly-funded incubators could contribute to strengthening STI-based entrepreneurship. India's STI policy and its links to societal goals span multiple decades -- but since 2015 these goals became formally organized around the SDGs. We examine why STI-based incubators were created under different policy priorities before 2015, the role of public agencies in implementing these policies, and how some incubators were particularly effective in addressing the societal challenges that can now be mapped to SDGs. We find that effective incubation for supporting STI-based entrepreneurship to meet societal goals extended beyond traditional incubation activities. For STI-based incubators to be effective, policymakers must strengthen the 'incubation system'. This involves incorporating targeted SDGs in specific incubator goals, promoting coordination between existing incubator programs, developing a performance monitoring system, and finally, extending extensive capacity building at multiple levels including for incubator managers and for broader STI in the country.