We formulate a consistent octonionic foundational model in which gravity, matter dynamics, and non-associative coupling arise from a common variational principle. The starting point is a set of physical minimal principles: the requirement of real observables, local dynamics, covariant formulation, positivity of a norm, minimal algebraic nontriviality, and the requirement that genuine triple couplings may be fundamental. From these principles it follows step by step that the relevant internal algebra must be a normed division algebra, and that the only finite-dimensional non-associative possibility is the algebra of octonions. Since non-associativity becomes visible only through the associator of three arguments, the minimal dynamical realization is a triplet of octonion-valued fields. On this basis the full covariant action is constructed, and its variation yields the coupled master equation: the Einstein equation together with three octonionic field equations sourced by the associator. Every term, coupling, and parameter is explicitly introduced and physically interpreted.