Scattered light imaging through complex turbid media has significant applications in biomedical and optical research. For the past decade, various approaches have been proposed for rapidly reconstructing full-color, depth-extended images by introducing point spread functions (PSFs). However, because most of these methods consider memory effects (MEs), the PSFs have angular shift invariance over certain ranges of angles. This assumption is valid for only thin turbid media and hinders broader applications of these technologies in thick media. Furthermore, the time-variant characteristics of scattering media determine that the PSF acquisition and image reconstruction times must be less than the speckle decorrelation time, which is usually difficult to achieve. We demonstrate that image reconstruction methods can be applied to time-variant thick turbid media. Using the time-variant characteristics, the PSFs in dynamic turbid media within certain time intervals are recorded, and ergodic scattering regimes are achieved and combined as ensemble point spread functions (ePSFs). The ePSF traverses shift-invariant regions in the turbid media and retrieves objects beyond the ME. Furthermore, our theory and experimental results verify that our approach is applicable to thick turbid media with thickness of 1 cm at visible incident wavelengths.