The sun is the source of virtually all energy on Earth. Thus climate has always strongly tracked solar activity. Numerous studies of many different types of data, covering many thousands to millions of years of Earth history bear this out.

In the last 35 years, the sun has shown a very slight cooling trend, while the Earth has warmed.

It ain't the sun, no matter what variable you choose to characterize "The Sun". The sun and Earth are going in different directions temperature-wise, but only over the last 35 years. In those same 35 years, human population approximately doubled. Correlation does not prove causation, but surely, even to the politically-motivated, that must suggest the possibility of a human influence.