I think your hypothesis ascribes meaning to an insignificant probability. The odds of virtually any micro event viewed from the universal perspective are, as you say, vanishingly small.
Correct, and we've brought up snowflakes, snowballs, bananas, Volkswagens, and individual North American mountains (Ranier is the favorite) as examples of items that exhibit individual variation in their emergent properties owing to chaotic elements in the processes that form them.
Jabba insists that consciousness, or self-awareness, is a special property unlike any other kind of emergent property of any other kind of matter, and thus can't be considered equivalent to any of those other examples. He will offer you a whole web of special pleading to support that insistence.
I should not that I may appear to differ from some of my colleagues in that I deny the individuality of self-awareness. That is, I argue that the property of self-awareness, consciousness, or whatever name you want to apply, is the same for all properly-formed humans. We are all self-aware. Each of us is self-aware in exactly the same way as another. This is illustrated by the property of a car on the freeway, that it "is going 60 mph." This is true of all cars going that speed, and there is not an individualized difference between the "going 60 mph" of one car and the "going 60 mph" of another car. The cars are obviously individuals, but the property is not. It is not discretizable.
My colleagues seem to fully agree with the above, but for some purposes wish to conflate such things as sensory input and memories into the observation of self-awareness. In materialism, memories are stored in the brain as chemical and physical configurations of the brain's physiology. But then again in materialism, self-awareness and consciousness are the product of properties exhibited by that same brain physiology, so an argument can be made that the process named by the property should be individualized accordingly. It's not a big deal, of course, but you should be advise of it.