The play "Book of Mormon" has a pivotal scene where Joseph Smith, in a pique of abandonment, accepts that the obvious solution of showing the Golden Plates to everyone is not available to him.
The Book of Mormon itself has the answer to that. When confronted with the idea of seeking scholarship to substantiate the Book of Mormon, God replies He can do his own work, and doesn't need to rely on the fame and reputation of us mere mortals. The success of the book, relying solely on people praying to know its true, shows plain evidence to that.
But even more important is the personal angle, how does that apply to me and the things I need right now?
We feel the need to fight our way out of bad situations, when what we really need is to be rescued, to let God do his own work in and through us. And the Book of Mormon, more than answering the potential critics of how God worked with Joseph Smith with a few verses, gives that constant theme throughout the Book of how God works with every one of us, to rescue us from our own limitations and harm.
That leaves the proof in a very personal space, where you learn through the experience of help through what you know are completely out of your own abilities. What you learn is the definition of 'faith', and that help is the definition of 'grace'.