The COVID-19 pandemic is a national tragedy, one that has focused our attention on both the need to improve science education and the need to confront systemic racism in our country. We know that active learning strategies, in particular research experiences, can engage and empower STEM undergraduates, effectively closing the achievement gap for historically excluded persons. The apprenticeship model for STEM training - supervised research under a dedicated mentor - is highly effective, but out of reach for most students. Recent efforts have demonstrated that Course-based Undergraduate Research Experiences (CUREs) can be an effective approach for making STEM research accessible for all. Our meta-analysis of CUREs finds that published examples now cover the breadth of the typical undergraduate biology curriculum. A thoughtfully designed CURE can go beyond foundational knowledge and analytical thinking to include career-related skills, e.g., teamwork and communication. Similarly, it can be designed with equity as a foundational principle, taking into account the unique contributions of all students and their varying needs. We provide here an example framework (The "Do Science Framework") for making STEM training more effective and inclusive using CUREs. While CUREs do not inherently address equity, there can be no equity in STEM education without equal access to research participation, and progress toward this goal can be achieved using CUREs. However, implementing new CUREs is not a trivial undertaking, particularly at schools with high teaching loads and little or no research infrastructure, including many community colleges. We therefore propose a National Center for Science Engagement to support this transition, building on experiences of current nationally established CUREs as well as the work of many individual faculty. In the aftermath of the COVID-19 pandemic, academia has a renewed responsibility to dismantle structural inequities in education; engaging all STEM students in research can be a key step.