Social innovation has broadly been defined as citizen-led initiatives aimed at improving community welfare through collaborative relationships. However, numerous studies demonstrate that social innovation might actually create new inequalities. In this paper, we address the following questions: how might socially innovative projects influence public policy? How can we understand a policy shift leading to institutions not only giving support to social innovation projects but even promoting their own social innovation schemes? Is institution-led social innovation different from citizen-led efforts? If so, how? We provide evidence of local public policy change occurring in 0–3 education and care in Barcelona between 2015 and 2021. We explain how this happened, examining who redefined the issue and how, how the policy domain was reorganized, and how the policy subsystem was restructured. Our conclusions show how and why citizens and institutions define social innovation differently and how innovative 0–3 policy in Barcelona was adopted.