Cells somehow evolved from primordial chemistry and their emergence depended on the co-evolution of the cytoplasm, a genetic system and the cell membrane. It is widely believed that the cytoplasm evolved inside a primordial lipid vesicle, but here I argue that the earliest cytoplasm could have co-evolved to high complexity outside a vesicle on the membrane surface. An invagination of the membrane, aided by an early cytoskeletal system, may have formed the first cells--initially within primordial vesicles.