Data physicalization, which encodes data in physical form, has been increasingly used to engage the public with issues of social good. While public engagement is often invoked as a motivation or expected outcome, it has not been systematically examined as a design objective. This gap raises two key challenges: what characterizes engagement in data physicalization for social good (Phys4Good), and how it can be effectively designed. In this work, we address these challenges by first curating a corpus of 45 Phys4Good projects and deriving a design space structured around a modified three-act framework comprising Stage, Encounter, and Impact. We then conducted semi-structured interviews with designers of eight projects to identify recurring challenges and strategies for fostering engagement. Finally, we demonstrated the effectiveness of our design space and strategies through a case study, which showed that they can guide designers in structuring engagement, anticipating barriers, and creating more impactful Phys4Good experiences.