This article provides an account of the making of KBLab, the data lab at the National Library of Sweden (KB). The first part discusses the work involved in establishing a lab as both a physical and a digital site for researchers to use digital collections at previously unimaginable scales. The second part explains how the lab has deployed the library's collections as data to produce high quality Swedish AI models, which constitute a significant new form of digital research infrastructure. We situate this work in the context of uneven AI coverage for smaller languages, and consider how the lab's models have contributed to the making of important AI infrastructure for the Swedish language. The conclusion raises the possibilities and challenges involved in continuing this type of library-based AI development.