Wikipedia has a pretty good summary of climate proxies (1). E.g., tree rings, coral, pollen, forams/ostracods/coccolithophores/radiolaria, varves/lake sediments, water isotopes, membrane lipids, etc. See also Wikipedia article re. temperature proxies, 'Paleothermometer'(2).
So, yes, we do have proxies for past climates and rates of change. Yes, there have been some pretty spectacular excursions in climate (e.g., the entry into the Younger Dryas happened within 50 years, and brought the climate of Nome, Alaska to San Francisco). However, I saw a research presentation that compared the rate of change in the Paleocene-Eocene Thermal Maximum (PETM) to Homo sapiens' injection of CO2 into the atmosphere, and the rate of our injection beat the PETM, and it may very well exceed any such injection in Earth's history (the latter is my speculation).
Tree rings tell us there were years where there was more or less rainfall relative to what that tree/forest normally sees - but it does not provide a measurement of how much water/rainfall there was. Different geographical regions experience different norms over time as well.
Same with temperature. We can infer there were hotter years, and colder years within those regions all throughout history. Being able to say the temperature averaged say 30*C was not possible until relatively recently.
It's all observational science, and we can't observe all of the factors unfortunately so we have to infer a great deal.
So, yes, we do have proxies for past climates and rates of change. Yes, there have been some pretty spectacular excursions in climate (e.g., the entry into the Younger Dryas happened within 50 years, and brought the climate of Nome, Alaska to San Francisco). However, I saw a research presentation that compared the rate of change in the Paleocene-Eocene Thermal Maximum (PETM) to Homo sapiens' injection of CO2 into the atmosphere, and the rate of our injection beat the PETM, and it may very well exceed any such injection in Earth's history (the latter is my speculation).
(1) Proxy (climate), https://en.wikipedia.org/wiki/Proxy_(climate) (2) Paleothermometer, https://en.wikipedia.org/wiki/Paleothermometer