The increasing importance of Computational Science and Engineering has highlighted the need for high-quality scientific software. However, research software development is often hindered by limited funding, time, staffing, and technical resources. To address these challenges, we introduce PyPackIT, a cloud-based automation tool designed to streamline research software engineering in accordance with FAIR (Findable, Accessible, Interoperable, and Reusable) and Open Science principles. PyPackIT is a user-friendly, ready-to-use software that enables scientists to focus on the scientific aspects of their projects while automating repetitive tasks and enforcing best practices throughout the software development life cycle. Using modern Continuous software engineering and DevOps methodologies, PyPackIT offers a robust project infrastructure including a build-ready Python package skeleton, a fully operational documentation and test suite, and a control center for dynamic project management and customization. PyPackIT integrates seamlessly with GitHub's version control system, issue tracker, and pull-based model to establish a fully-automated software development workflow. Exploiting GitHub Actions, PyPackIT provides a cloud-native Agile development environment using containerization, Configuration-as-Code, and Continuous Integration, Deployment, Testing, Refactoring, and Maintenance pipelines. PyPackIT is an open-source software suite that seamlessly integrates with both new and existing projects via a public GitHub repository template at https://github.com/repodynamics/pypackit.