Stable detection of high-speed dim point targets remains a key performance bottleneck for space-based infrared systems. During non-propulsive flight, such targets exhibit extremely weak infrared emissions, high velocities, and low imaging SNR, which severely limits the persistent detection capability of Geostationary/High Earth-orbit platforms and motivates exploitation of the slant-to-space geometry available to low-Earth-orbit (LEO) platforms. This research formulates the problem from the physical imaging chain of a LEO infrared system and develops a multi-parameter joint optimization model that systematically integrates target-background radiation, optical imaging design, and detector-level physical constraints. At its core is a normalized, weighted multiplicative merit function that enables global optimization of key system parameters, including spectral bandwidth, center wavelength, detector operating temperature, optical angular resolution, aperture diameter, and optical system temperature. Using a representative LEO long-wave infrared detector configuration, we conduct parameter search and end-to-end performance simulations. The optimized configuration produced by the proposed method enables stable detection of non-propulsive, high-speed dim point targets, achieving a best detection sensitivity of 1.036 W/sr@4000 km. This research provides both a theoretical foundation and a practical pathway for system-level optimization of LEO long-wave infrared detection systems.