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Adeno-associated viruses (AAVs) hold tremendous promise as delivery vectors for clinical gene therapy, but they need improvement. AAVs with enhanced properties, such as more efficient and/or cell-type specific infection, can be engineered by creating a large, diverse starting library and screening for desired phenotypes, in some cases iteratively. Although this approach has succeeded in numerous specific cases, such as infecting cell types from the brain to the lung, the starting libraries often contain a high proportion of variants unable to assemble or package their genomes, a general prerequisite for engineering any gene delivery goal. Herein, we develop and showcase a machine learning (ML)-based method for systematically designing more effective starting libraries — ones that have broadly good packaging capabilities while being as diverse as possible. Such carefully designed but general libraries stand to significantly increase the chance of success in engineering any property of interest. Furthermore, we use this approach to design a clinically-relevant AAV peptide insertion library that achieves 5-fold higher packaging fitness than the state-of-the-art library, with negligible reduction in diversity. We demonstrate the general utility of this designed library on a downstream task to which our approach was agnostic: infection of primary human brain tissue. The ML-designed library had approximately 10-fold more successful variants than the current state-of-the-art library. Not only should our new library serve useful for any number of other engineering goals, but our library design approach itself can also be applied to other types of libraries for AAV and beyond.