The word Qur'an means "recitation", the Qur'an was not intended as a book. I'll go over the basics here.
A verse would be revealed to Muhammad ص
He would recite it, and teach it to his companions
He had several scribes, he would have them write it, to teach other people
When Muhammad ص died, the Qur'an was written, probably a few times over on these fragments. During the first caliph, Abu Bakr's reign, he tasked after the battle of Yamamah in which many Haafiz (people who fully memorized the Qur'an) died, Zayd ibn Thaabit with collecting all those fragments from the scribes, and each fragment needed two credible witnesses to authenticate it was indeed written on the command of the prophet.
This is how the first codex of the Qur'an was compiled.
Uthman, later standardized the harf into the original Qurayshi harf (there were six others, in six other dialects revealed to Muhammad ص). He did this because in foreign lands they would argue over who has the correct version, even though both were correct, to clear up confusion, the original harf was distributed to the conquered provinces.
And that's really the end of the story as simplified as I could make it.
Muhammad's ص literacy makes the Qur'an miraculous because he could not read the Abrahamic scriptures yet the Qur'an is filled with the stories of Adam, Abraham, Moses, Jesus, Lot, Job, Noah etc. So in order to naturally explain the existence of the Qur'an we need to find a historical link between highly educated scriptural scholars, and Muhammad ص and even then it does not explain how Muhammad came up with these stories in the form of poetry he did, which was reveered by the Arabs who were very into poetry... and furthermore how did he, Muhammad ص a Qurayshi then give the Qur'an in six different dialects for different Arabs, who were from different tribes? Was Muhammad an Arabic expert and a poet? Where's the historical link?
My point is simple, it would take a committee (even in modern times), to produce something like the Qur'an. You would need at the bare minimum, scholarly knowledge of the biblical scriptures, an expert in Arab poetry, and know many regional dialects of Arabic to disseminate the Qur'an to different Arab tribes.
How did Muhammad ص do it then?