I missed the same experience by "... that much!" (best Don Adams/"Get Smart" imitation.)
I was bird hunting on the side of a smallish Maine Mountain, where several terraces descend to the valley like a giant's staircase. I was taking a break in the October sun, late in the morning, sitting on one of the 'steps' with shotgun across my lap, when I heard 'the rustle in the leaves that ISN'T a squirrel.'
I sat immobile, not daring to blink, as a young doe approached along the terrace where my feet were resting and came within a yard of me, moving a slow step at a time; uncertain of this strange lump sitting in her woods. At the moment of her closest approach I could have easily touched her with my hand.
Closed season, and she was too beautiful to kill. I blinked, and she started, jumping away to about 15 feet. Still unsure, she walked away slowly, continuously looking back as if in wonder of what had frightened her. I treasure the memory. For a while I knew what it was like to be the invisible man. (This was before blaze orange, and before camo. I was wearing green wool logger pants and a gray and blue plaid mack. I think I did have an orange hat, back then, but it was far more likely to be an old black French beret that I fancied at that time.)