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. 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, we can quantitatively determine the conditions for SBS generation, 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 remains significant discrepancies in reported conclusions regarding the relationship between incident energy levels and pulse width variations, particularly in water-based environments where systematic investigations on Stokes scattering pulse characteristics are notably absent. In this study, based on a distributed noise model, we conducted theoretical simulations and analyses of the time-domain signals of SBS in water for different laser wavelengths, pulse widths, and focal lengths. We investigated the characteristics of Stokes pulses generated by both focused and non-focused configurations. The results indicate that shorter incident wavelength produces significantly higher peak power of Stokes scattered light under the same conditions. The Stokes scattered light exhibits distinct energy-dependent behavior: at low input energies, short pulses generate stronger scattered signals due to enhanced nonlinear interaction efficiency, whereas at high input energies, longer pulses exhibit superior performance by maintaining temporal coherence. The larger focal lengths result in lower peak power but better pulse fidelity. As the incident energy increases, the pulse width of Stokes scattered 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 superior compression performance near the threshold energy. Therefore, for short-range SBS-Lidar applications, mitigation of secondary peak interference and suppression of spectral broadening are critical technical challenges that must be systematically addressed. In low-temperature detection scenarios, dynamic attenuation control becomes essential to prevent thermal stress-induced damage to photodetectors. These findings are of great significance for enhancing the performance of SBS-LiDAR system.