My understanding is that, while you are correct that these emissions are already in the air, they filter themselves out over time, so it's about rates of production vs rates of dismission (for lack of a better word). If we stop all emissions today, the sky will quite literally start clearing up, and thus warming the Earth even more.

Not trying to be too sensationalist, but I believe this is the truth.

They're on different timescales. The aerosols will come out of the atmosphere relatively quickly, causing rapid warming.

Here's the original article I was recalling: https://science.sciencemag.org/content/363/6427/eaav0566/tab...

The IPCC working group 1 summary talks about the physical effects, that's a pretty good primary source if you want a lot of detail and tons of references to trace down.