It’s obvious.
The sun provides 99.998% of the energy to the Earth’s climate (the rest coming from geothermal heat sources). The circulation patterns of the tropical Hadley Cell, the mid latitude storm tracks the polar high and the resulting climate zones are all driven by the gradients of solar heating as a function of latitude. So of course any significant change to solar output is bound to affect the climate, it stands to reason! Since we can see that there are changes in solar activity, it’s therefore just a question of finding the link. Researchers for over a century have therefore taken any climate records they can find and searched for correlations to the sunspots, the solar-cycle length, geomagnetic indices, cosmogenic isotopes or smoothed versions thereof (and there are many ways to do the smoothing, and you don’t even need to confine yourself to one single method per record). At the same time, estimates of solar output in the past are extremely uncertain, and so there is a great deal of scope in blaming any unexplained phenomena on solar changes without fear of contradiction.