> We know about the state of the world back then. We have history, archeology, the knowledge of that era, and much much more.

You don't know everything about that time. Do you have a recording of everything that was communicated between any party? Historical texts and archeology give us snippets from that time. We can get some general idea but we can't make absolute claims about every detail with 100% certainty.

  > Even the non Muslims admit and are in awe of what happened.

Some.

  > He proved that what's written in the Quran correct, discoveries made just a couple of hundred years ago. 

You can claim that a million more times. I saw no proof.