Data spaces are one of the key technology pillars of the European Strategy for Data, which intends to establish a single market inside the European Union (EU) for the efficient and secure sharing and interchange of data across industries. A data space that could combine and correlate cross-sector knowledge from the healthcare and environmental sectors could play a crucial role in determining the future of healthcare. Given that climate change is the single greatest health threat facing humanity and that health professionals worldwide are already responding to the health harms caused by this developing crisis, such a solution would enable the identification and correlation of environmental influences on human health as well as the extraction of novel biomarkers. However, the difficulties in creating such infrastructure necessitate cutting-edge, multidisciplinary research in numerous fields. This manuscript contributes into providing a visionary approach toward a single-entry point ecosystem to access, share, and trade cross-sector data assets originating from the environmental and healthcare domains through a Cross-sector Data Space (CDS), thereby effectively promoting European technological autonomy in data sharing. This CDS will consider a variety of analytics as ready-to-use solutions to facilitate analysis, prediction, and monitoring of the causality, correlation, reasoning, and practical visualization of real-time environmental settings, as well as to identify the effects of climate change to human health.