God (Allah) is the creator of all creations, He sent Prophets to guide the people, and those Prophets were believed and followed because they were supported by Miracles. One of the great miracles of Prophet Muhammad (Peace be upon him) is al-Qur'an.
First of all:
1. Prophet Muhammad challenged the tribes who had articulated the Arabic language to come up with one verse of the shortest verses of the Quran, and they couldn't do that. The Quran is such a very rich language, that it's impossible for a man to be able to make it up. If they were able to do that, they would have saved themselves and their tribes, from the blood shed and met the challenge, but they didn't.
So the Prophet came to challenge the people of Quraysh with the Quran. How? The Arabs back than had articulated the Arabic Language and mastered it, and Prophet Muhammad (May peace and blessings be upon him and all Prophets and messengers) was known to be unlettered, that is he did not read or write what is read and written. And he called people to Islam.
Among his miracles that prove his truthfulness, was the Quran. He came with this great challenge; with the Quran, which is known to have very rich words. The people could not meet the challenge. If they were able to meet the challenge of the Prophet, and come up with one short verse that meets or equals one that's from the Quran, they would have saved themselves from the bloodshed.
So, the Quran cannot be human-made, or angel-made. It's the speech of Allah that is unlike the speech of the creation. The Arabic words that we read in the Holy Book of the Quran are expressions of the Eternal speech of Allah which is not a letter or sound, because Allah does not resemble the creations in any way.
2. Prophet Muhammad was unlettered. The Quran is revealed in a rich language. At the time when the Arabs were very articulate in the Arabic language, they were known for that, and they were strong in poetry. It's well known that Prophet Muhammad was raised as an orphan, he did not learn from knowledgeable or clever people. Rather, he was a Prophet with miracles.
3. One remarkable feature of the Quran is its content of an abundant amount of scientific information. Much of this information has only been discovered by mankind in the last century. If this points to anything, it certainly indicates that the Quran could not have been written by any human being. When the Quran was revealed to Prophet Muhammad 14 centuries ago, there simply was no human being who had any access or knowledge of such scientific knowledge. The scientific information in the Quran covers main fields of knowledge.
4. And finally, among the intellectual proofs that it's intellectually impossible that the Quran is made up by Prophet Muhammad, or by a human, are the facts and the astonishing information and news in the Quran about previous nations and previous Prophets and about future events which he had foretold about such as the fall of the Roman empire and many other events. This all proves that he was the Prophet and messenger of Allah.
Note: The Qur'an is not man-made. It pertains the orders of Allah. The Qur'an we read now, is in a language that we understand. But the speech of Allah is neither a letter, language, or sound. But what we read in the holy books, are expressions of the eternal speech of Allah. Because Allah does not resemble the creations in any way.