Voluntary movement in animals is driven by the contraction of myofibrils in striated muscle cells, which are linear chains of regular cytoskeletal units termed sarcomeres. While the ordered structure of mature sarcomeres, key to muscle contraction, is well established, the physical mechanism governing sarcomere assembly is still under debate. Here we put forward a theory of sarcomere self-assembly based on data. We measured the sequential ordering of sarcomere components in developing Drosophila flight muscles, using a novel tracking-free algorithm. We find that myosin molecular motors, α-actinin cross-linkers, and the titin homologue Sallimus form periodic patterns before actin filaments become polarity sorted. Based on these, we propose that myosin, Sallimus, and sarcomere Z-disk proteins including α-actinin dynamically bind and unbind to an unordered bundle of actin to establish an initial periodic pattern. Periodicity of actin filaments is established only later. Our model proposes that nonlocal interactions between spatially extended myosin and titin/Sallimus containing complexes, and possibly tension-dependent feedback mediated by an α-actinin catch bond, drive this ordering process. We probe this hypothesis using mathematical models and derive predictive conditions for sarcomere pattern formation to guide future experiments.