The EVERSE project addresses the urgent necessity for dependable, high-quality, and sustainable research software within Europe’s scientific community. It brings together researchers, Research Software Engineers (RSEs), and other stakeholders to create a collaborative, community-driven framework for evaluating, verifying, and improving software quality. Through the launch of the EVERSE Network of Research Software Quality, the project has established a lasting structure for knowledge exchange and coordination, laying the foundation for a future Virtual Institute for Research Software Excellence. Key tools like the RSQKit and TechRadar offer selected best practices, tools, and validation steps, along with a complete training platform that builds skills and encourages the regular use of quality standards in different fields. By using and integrating current resources within the EOSC Science Clusters, EVERSE aims to standardise software quality practices and include ongoing evaluation processes in daily research activities. The project also encourages sustainability and acknowledgement by creating systems to give credit to RSEs and researchers for their work, linking these credits to established platforms like ORCID. In doing so, EVERSE builds a culture of excellence, collaboration, and long-term impact, ensuring that European research software is not only technically sound but also openly shared, reusable, and properly valued as a cornerstone of reproducible science.