Biological materials have attracted a lot of attention due to their simultaneous superior stiffness and toughness, which are conventionally attributed to their staggered structure (also known as brick and mortar) at the most elementary nanoscale level and self-similar hierarchy at the overall level. Numerous theoretical, numerical, and experimental studies have been conducted to determine the mechanism behind the load-bearing capacity of the staggered structure, while few studies focus on whether the staggered structure is globally optimal in the entire design space at the nanoscale level. Here, from the view of structural optimization, we develop a novel long short-term memory (LSTM) based iterative strategy for optimal design to demonstrate the simultaneous best stiffness and toughness of the staggered structure. Our strategy is capable of both rapid discovery and high accuracy based on less than 10% of the entire design space. Besides, our strategy could obtain and maintain all of the best sample configurations during iterations, which can hardly be done by the convolutional neural network (CNN)-based optimal strategy. Moreover, we discuss the possible future material design based on the failure point of the staggered structure. The LSTM-based optimal design strategy is general and universal, and it may be employed in many other mechanical and material design fields with the premise of conservation of mass and multiple optimal sample configurations.