Anyone who has been involved in apologetics discussions has probably seen this same argument from both Muslims and Christians.
We can confirm with extra-Quranic sources that Muhammad did indeed conquer Mecca
This verifies the Quranic claim that Muhammad conquered Mecca
Therefore, the Quran is proved.
Since the Quran is proved, this in turn proves all the other truth claims in the Quran.
Therefore it is proved that Muhammad flew a winged horse into outer space just as claimed in the Quran. Because I proved the Quran, and that proves that everything in the Quran is true.
Except, that's not how any of this works. That's now how proof works, and that's not how historical claims work.
Your holy book is not supporting evidence for truth claims
One thing that theists find disturbing is that people outside their religion do not automatically regard everything in their holy book as true. If you find this disturbing, I don't care. I'm sorry to be blunt, but I don't. Whether you are Christian or Muslim or any other religion, your holy book is not supporting evidence for truth claims, it is yet another set of truth claims that you have to prove.
This brings us back to the above argument: attempts by Muslims and Christians to "prove the Bible" or "prove the Quran." Christians and Muslims seem to feel that if they can verify individual facts from the holy book, then the holy book is therefore "proved" and therefore everything else in the holy book is demonstrated to be true.
We can prove through extra-Quranic sources that Muhammad conquered Mecca. What many Muslims fail to grasp is that doing so only verifies that one specific claim from the Quran. Similarly, finding an ancient stone with the name "David" on it does not "prove the Bible." At most, this verifies that there once existed a man named David; it does not prove that a zombie army rose out of their graves and wandered the streets of Jerusalem.
Every single work of historical fiction includes a large number of facts from the real world that are true and corroborated by sources outside that work of fiction. We can prove that Springfield, Illinois is a real place and that the Civil War actually happened, but that does not prove that Abraham Lincoln was a vampire-hunter. We can prove that Queens is a real place in New York, but that doesn't prove that Spider-Man is real.
The existence of a city named Mecca doesn't prove Muhammad flew into outer space on a winged horse any more than the existence of a city named Jerusalem proves that Jesus flew into outer space without a winged horse. You don't "prove" a book, you prove individual claims from a book.