And if there were a way to prove Hashem’s existence, it wouldnt be a nisayon.
But in reality it is, and that also accounts for so many mitzvot surrounding the subject. However, just because one cannot prove that Hashem exists does not mean that there is not a tremendous amount of evidence that He does.
In a kuzari class I attended in Yeshiva, the Rebbe explained that it is a “modern” philosophical concept that everything must be proven beyond the shadow of a doubt (Renee De’Carte “I think therefore I am”) and that lehavdil even in the American Judicial System our goal is only “Beyond a reasonable doubt” and if I could underline reasonable I would… and that is what begins the process of opening one’s mind to Hashem. Eventually you hope they reach the point once they become open minded that they no longer need proof because they’ve experienced it already.
I would start going through the evidence but like I said, there are books out there that say it much more eloquently than I am capable of.