The Quran is the evidence. It claims that it cannot have been written by men, that it was inspired by God.

It even goes so far as to challenge humans to produce one chapter like it, and says that we never could. Since doing so would require the writer to claim that God has inspired it, this will not be an easy task.

The Quran states that:

"What is the matter with you that you do not regard the greatness of Allah when He has created you in gradual stages?" (Quran 71:13-14)

I know some Muslims do have a problem with evolution, but it is not the process of evolution which is the problem. The Quran clearly indicates that this is the way God creates. The problem is that evolution is taught without mentioning even the possibility of a designer.

Understanding the Quran is a whole study, which I don't feel like I can do justice to here, without knowledge of Arabic etc...

If you have a problem with my understanding, I would recommend doing your own research. I can't prove my religion to you, just like you can't prove that there is no God. But I have studied it a lot, and I can find no reason to believe that the Quran was written by any other than God, as it claims.

I don't have any problem with teaching evolution as a theory in a mosque.