This Oral tradition theory of Quran is a fraud..........Quaran was compiled by MastRam paanwala....and is compilation od Baddu Baakchodi by his clients !
You are asking a "loaded" question and the answer is not simply yes or no.
The best answer to your question is the unbroken chin of Memorizers of Quran, starting from prophet till this day, which is the best proof.
There NEVER was any time, when hundreds of thousands of memorizers of Quran were not existing in every part of the world.
Get a Blind man from China who has memorized full Quran and bring a Pure Arab from Makkah who has memorized the Quran.
Let them recite Quran in front of you, there would be no change in their wordings and even punctuation marks. This is Quran.
As for as written copies of complete Quran go. We reach to the stage where Third Caliph of Islam, made authentic copies of Quran in year 29-30 AH (i.e. just 19-20 years after death of Prophet) in front of thousands of companions of prophet.
I am not ducking around. It is you people who trying to "get around your guilt" by asking tests about Quran, which NONE of books in the world can meet.