Stimulated Brillouin scattering lidar (SBS-LiDAR) technology possesses significant advantages such as high resolution, high signal-to-noise ratio, and strong anti-interference capacity, making it highly promising for simultaneous measurements of temperature, salinity, and sound velocity in seawater. Stimulated Brillouin scattering (SBS) is a nonlinear dynamic process characterized by temporal variations in its occurrence location, peak intensity, and spectral shape. Through numerical simulations of Stokes pulse, the conditions for SBS generation can be quantitatively determined, thereby establishing a theoretical foundation for optimizing lidar systems and enhancing their detection capabilities. Existing studies on Stokes pulses typically focus on specific experimental configurations under varying parameters, including medium properties, pump laser characteristics, and ambient environmental factors. There are still significant discrepancies in reported conclusions regarding the relationship between incident energy levels and pulse width variations, particularly in water-based environments where systematic research on the Stokes scattering pulse characteristics is clearly insufficient. In this study, a distributed noise model is used to theoretically simulate and analyze the time-domain signals of SBS in water at different laser wavelengths, pulse widths, and focal lengths. The characteristics of Stokes pulses generated by focused and non-focused configurations are investigated. The results indicate that under the same conditions, shorter incident wavelength produces significantly higher peak power of Stokes scattering light. The Stokes scattering light exhibits significant energy-dependent behavior: at low input energy, short pulse generates stronger scattering signal due to enhanced nonlinear interaction efficiency, while at high input energy, longer pulse exhibits excellent performance by maintaining temporal coherence. The larger focal length results in lower peak power but better pulse fidelity. As the incident energy increases, the pulse width of Stokes scattering light in the non-focused configuration exhibits a continuous increase. In contrast, for the focused configuration, the pulse width initially decreases and then increases, exhibiting an optimal compression value influenced by temperature and energy. At lower temperatures, the Stokes pulse width exhibits excellent compression performance near the threshold energy. Therefore, reducing secondary peak interference and suppressing spectral broadening are critical technical challenges that must be systematically addressed for short-range SBS-Lidar applications. In low-temperature detection scenarios, dynamic attenuation control becomes essential to prevent thermal stress-induced damage to photodetectors. These findings are of great significance in enhancing the performance of SBS-LiDAR system.