There is no non-miraculous explanation for the Miracle of the Sun at Fatima. It is impossible to investigate the facts and remain a non-believer. That is why non-believers don't investigate Fatima. They keep their non-belief intact through avoidance.
I'll tell you what is impossible.
The desire to believe is one of the most powerful psychological forces in humanity, and almost always impossible to overcome.
We see even today that people see and hear what they want to see and hear, and willfully ignore evidence which violates their belief system.
The facts are that despite there being a horde of reporters and photographers, there was no photography taken, or reportage, of the claimed event of the sun dancing around and changing its composition. Nor was there any mention of an oddly behaving sun from anywhere else on Earth the sun was visible at the time.
Eyewitness reports are inconsistent and contradict each other. Many eyewitnesses reported seeing nothing. This is evidence of data having been cherry-picked which only confirmed the paranormal claims and ignoring data which did not conform.
The one and only photo supposedly taken during the event is actually a photo from eight years later in a different town in Portugal.
1917 was a very different and very difficult time. The world had been involved in three years of a devastating global war, unprecedented in its scale. The people were looking for hope. In the midst of all that slaughter and carnage, they needed a sign from above that God gives a shit about them, pardon my French.