The good news is that correcting the climate problem caused by soot would be easier than dealing with methane and carbon dioxide. Soot is a solid, so it is removed from the atmosphere much more quickly than either methane or carbon dioxide. Within weeks of soot’s emission, it simply falls to the surface of the earth, whereas carbon dioxide and methane may hang around in the atmosphere for years. In addition, most of the soot comes from diesel engines, inefficient stoves, and dirty diesel fuel; all problems that could be dealt with fairly easily if we had the will to do so. Improving the efficiency of diesel engines to reduce soot emissions would have a significant impact within weeks.
You can read the entire comprehensive study of soot and its role in climate change in the Journal of Geophysical Research: Atmospheres. But I warn you; it’s 286 pages long! For a quick look, read the abstract.