First off, what makes the Bible any more likely to be true than the Qur'an? I want you to explain that. And now I'll explain how apes evolved into humans: Apes, because of climate change, moving to a location with a different climate, or being put in conditions they are not used to, caused a very minor and isignifigant resistance, strength, protection, or any change to their body that could not be told even existed. If they were to have children, their children would be born with the same effect from the conditions. The effect would grow stronger in that child, and in their children, and so forth, and over the course of millions of years the effects would become noticeable. Apes had to have multiple effects on them, because there is more than 1 difference between hummans and apes.
On some rare occasions, there could be something called a genetic mutation. A macroscopic difference that came just between parents and children. For example, the woman with horns, the first orange carrot in the 1700s, and the girl with purple eyes. I hope that gives a clear explanation on how "an ape could do that", even though it took much more than an ape.