Gordon,
No, there is no definitive proof that aerosols caused the cooling. This is true. But it is the only theory that matches the observed facts so far. It appears quite likely that the aerosols cooled the planet, but remember that science does not deal in absolute proofs.
Remember, other theories–the oceans, the sun–have been falsified for that period.
Re: 1920-1930 I don’t know why it is vague. CO2 was rising as was solar irradiance and this caused a slight warming.
50 years is fine, as is 100. The key is that the period must be long enough so that internal weather fluctuations roughly cancel out. 30 years is enough time to do that. If you do an analysis over shorter time frames, you have to take into account ocean fluctuations and other weather “noise”. If we had reliable temperature readings going back 1000 years, that would fine too.
