This paper investigates the spatial–temporal cooperative guidance problem for multiple flight vehicles without relying on time-to-go information. First, a two-stage cooperative guidance strategy, namely the cooperative guidance and the Proportional Navigation Guidance (PNG) stage strategy, is developed to realize the spatial–temporal constraints in two dimensions. At the former stage, two controllers are designed and superimposed to satisfy both impact time consensus and impact angle constraints. Once the convergent conditions are satisfied, the flight vehicles will switch to the PNG stage to ensure zero miss distance. To further extend the results to three dimensions, a planar pursuit guidance stage is additionally imposed at the beginning of guidance. Due to the independence of time-to-go estimation, the proposed guidance strategy possesses great performance in satisfying complex spatial–temporal constraints even under flight speed variation. Finally, several numerical simulations are implemented to verify the effectiveness and advantages of the proposed results under different scenarios.