I know that the ice cores studied by science show the last cycle was much worse than the current one and occurred about 40,000 years before anything man made could have had an impact on the environment....
I'm curious why you think that matters. What you are talking about is called
paleoclimatology and it is how we understand the NATURAL FORCINGS which affect climate. Since we know humans were not pumping exces CO2 into the atmosphere 40,000 years ago we can better understand what drives climate NATURALLY.
Unfortunately for you the NATURAL FORCINGS cannot be leveraged to explain the majority of the warming we see today. The sun is not in the right output phase, ocean currents are not dramatically shifting, etc.
But we can easily measure the amount of ADDITIONAL GREENHOUSE GAS pumped into the atmosphere (we can even see human fingerprints on it via the isotopic composition of the CO2, lots of 12-C vs 13-C indicative of fossil fuel burning and/or vegetal burning).
Right now the ONLY thing that can FULLY EXPLAIN all the warming we've seen in the last 60 years is more than 50% due to human activities.
Want to see some data? Here's a comparison of the last 150+ years of temperature fitted to ONLY NATURAL FORCINGS (doesn't fit well) and HUMAN FORCINGS (the fit greatly improves).
There's a role for natural forcings but right now humanity is carrying the majority of the burden of causing warming.
I know that science acknowledges there is nothing that mankind can do to cool the climate
Again, you're wrong. In the middle of the 20th century there was an anomalous cooling (mostly in the northern hemisphere) which has now been likely associated with human-caused sulfate aerosol pollution. It kicked off in the early 1940's (beginning of WWII and increases in industrialization) and ended in the 1970's when we finally cleaned up the air.
Impact of global dimming and brightening on global warming
Wild, M., Ohmura, A., & Makowski, K. (2007). Impact of global dimming and brightening on global warming. Geophysical Research Letters, 34(4).