The "I am" is the main peculiar thing- Consciousness. if you just based it on current known math (and science that I'm aware of), there is no obvious reason why there would be this consciousness phenomenon, which at least I experience (I have faith that many other people experience it but I have no hard evidence that they do). Is it emergent? Why? How? And how do we tell between a genuine one and one that's just simulated - or will consciousness magically emerge in all such simulations?
If you use the "Occam's Razor", why would there be need of this consciousness thing? We could be machines behaving like conscious creatures but not have consciousness. There's no need for it right? Or is there?
As for the simulation thing. It's why I think it's silly for people to be so sure there is no Creator of this universe. It's as silly as entities in a fancy computer game claiming that there is no Creator just because the internal rules of the computer game don't require the existence of one.. But yes you could reasonably claim that based on what you know of this universe's rules and information you _believe_ there is no Creator. But being _sure_ there isn't is a different thing.
Heck for all we know those Creationists might be right in a way and this particular universe instance could really have been created 6000 years ago ;). After all if those astrophysicists start a 13 billion year old universe simulation 5 minutes ago - is their universe simulation 5 minutes old or 13 billion years old?
But what if you run it at a slower/faster subjective time, stop, change things and restart it etc. How old is it then?
 Yeah I have faith you have an "imaginary friend" that you call "me", but I don't have hard evidence of it other than I experience the same thing and I don't think I'm that special. Even if one day scientists wire you up and turn stuff on and off it'll still be hard to prove things 100% - since they might just be turning off the ability to write to persistent memory the experience of consciousness and not the consciousness itself. You might actually still be conscious while you are asleep or under anesthesia, it could be just that you can't do much "read" or "write" from/to "main memory" - you might still experience stuff from your senses...