Atmospheric models forced with observed sea-surface temperatures (SSTs) suggest a trend toward a more-stabilizing cloud feedback in recent decades, partly due to the surface cooling trend in the eastern Pacific (EP) and the warming trend in the western Pacific (WP). Here we show model evidence that the low-cloud feedback has contributions from both forced and unforced feedback components, and that its time variation arises in large part through changes in the relative importance of the two over time, rather than through variations in forced or unforced feedbacks themselves. Initial-condition large ensembles (LEs) suggest that the SST patterns are dominated by unforced variations for 30-year windows ending prior to the 1980s. In general, unforced SSTs are representative of an ENSO-like pattern, which corresponds to weak low-level stability in the tropics and less-stabilizing low-cloud feedback. Since the 1980s, the forced signals have become stronger, outweighing the unforced signals for the 30-year windows ending after the 2010s. Forced SSTs are characterized by relatively uniform warming with an enhancement in the WP, corresponding to a more-stabilizing low-cloud feedback in most cases. The time-evolving SST pattern due to this increasing importance of forced signals is the dominant contributor to the recent stabilizing shift of low-cloud feedback in the LEs. Using single-forcing LEs, we further find that if only greenhouse gases evolve with time, the transition to the domination of forced signals occurs 10-20 years earlier compared to the LEs with full forcings, which can be understood through the compensating effect between aerosols and greenhouse gases.