The ongoing development of a Swiss Health Data Space (SHDS) presents an opportunity to transform health delivery and care by enabling large-scale secondary health research. The successful implementation of the SHDS depends on its trustworthiness, as public trust is closely linked to public participation in data-sharing initiatives. We conducted four focus groups across the German-, French-, and Italian-speaking regions of Switzerland to identify public expectations and requirements related to the attributes that define a trustworthy SHDS. The participants discussed four fictitious case studies on: (1) consent management; (2) record linkage via the national social security number; (3) national data coordination center; and (4) cross-border data exchange. To best inform Swiss policy, we held a panel discussion with patient experts and healthcare professionals to translate the focus group findings into governance and public communication recommendations. Policy recommendations are proposed based on insights from the fictitious case studies discussed with participants, accompanied by guidance on implementation measures that contribute to proactively building trust in the development of the SHDS. Communication recommendations are further provided, highlighting that the success of the SHDS will depend on early and continuous trustworthy public communication efforts that actively engage the Swiss public, address their concerns, and foster support throughout its development. Overarching these efforts will be a foundational governance approach that meaningfully involves relevant stakeholders and members of the Swiss public, while allocating appropriate responsibility to maintain trustworthiness of the SHDS.