Cognitive science is relatively young (compared to other branches) but it has made tremendous strides of late. What most people would call “spiritual” experiences can be replicated in the lab, even the sensation of “being in the presence of a god”. So, I do not doubt people have had experiences. But I doubt attribution to a supreme being as the source is required. If there is a simpler, more logical explanation, then that’s the likely answer (Occam’s Razor).
This relatively young branch of science has also, very recently, attributed the “spiritual” experiences many people have to specific brain damage or lack of development in certain areas of the brain.
So, here we sit. Logical, rational explanations vs “feelings”. Regarding “feelings”, remember that other faiths have them as well. They each believe them as strongly as any other. Which seems more likely?
Seventh (an interesting blurb on being a slave to emotion – with Muppet-type puppets)
Eighth (the Mormon Testimony – by a former Mormon)
And, of course, each of these links contains other references. This is only the tip of this iceberg. There is so much more. Google (seek) and ye shall find…