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We present a self-designing key-value storage engine, Cosine, which can always take the shape of the close to "perfect" engine architecture given an input workload, a cloud budget, a target performance, and required cloud SLAs. By identifying and formalizing the first principles of storage engine layouts and core key-value algorithms, Cosine constructs a massive design space comprising of sextillion (10³⁶) possible storage engine designs over a diverse space of hardware and cloud pricing policies for three cloud providers - AWS, GCP, and Azure. Cosine spans across diverse designs such as Log-Structured Merge-trees, B-trees, Log-Structured Hash-tables, in-memory accelerators for filters and indexes as well as trillions of hybrid designs that do not appear in the literature or industry but emerge as valid combinations of the above. Cosine includes a unified distribution-aware I/O model and a learned …