How should I explain the authenticity of The Holy Quran to a non Muslim?

Very simple answer if you go a book shop and ask him please give me Bible he ask you which Bible do you want?

Below are 12 of the common Protestant Bibles used today. Here is a list:
Amplified Bible (completed in 1965)
Christian Standard Bible (Completed in 2017)
Holman Christian Standard Bible (Completed in 2004)
The King James Bible (Completed in 1611)
The Living Bible (Completed in 1971)
The Message (Completed in 2002)
New American Bible (Competed in 1970)
English Standard Version (Completed in 2001)
New Living Translation (Completed in 1996)
New International Version (Completed in 1978)
New American Standard Bible (Completed in 1971)
New King James Version (Completed in 1982)

But if you travel to whole globe East and West, North and South you will find same quran with fractions differences. Why because when the revelations of the Qur’an began, the Most Noble Messenger clearly proclaimed the Qur’an to be the word of God, and said it was impossible for any human being to duplicate it. If anyone disagreed, he ought to make an attempt to copy it, and should feel free to seek help from any source in doing so. None was able to take up this challenge and produce even a short surah similar to the Qur’an.

The Qur'an remains a book of inimitable quality, not only from a linguistic, but also from and intellectual, point of view. When Muhammad (pbuh) was challenged by his fellow countrymen to present a miracle, in keeping with the tradition of other prophets, he presented the Qur'an to them. The inimitability of the Qur'an is repeatedly emphasized in the Holy Book itself.

The Qur’an issued a challenge not only to the contemporaries of the Prophet (pbuh) but also to men in all ages. In order to demonstrate the incapacity and impotence of people to imitate it, it issued the following universal proclamation:

“Were all mankind to come together and wish to produce the like of the Qur’an, they would never succeed, however much they aided each other”. (17:88)

It then modifies the challenge and reduces its scope by saying:

“Do people imagine that this Qur’an is not from Us, and that you, O Prophet are falsely attributing to us? Tell them that if they are speaking truly they should produce ten surahs resembling the Qur’an, and that they are free to call on the aid of anyone but God in so doing.” (11:13)

Then, at the third stage, the scope of the challenge is reduced still further: the deniers are called on to produce only a single surah resembling the Qur’an:

“Oh people, if you doubt the heavenly origin of this Book which We have sent down to Our servant, the Prophet, produce one surah like it.” (2:23)

A yet stronger challenge occurs in another chapter:

“Or do they say: 'He forged it'? Say: 'Bring then a sura like unto it and call [to your aid] anyone you can”. (10:38)

Since we know that some of the shorter surahs consist only of a few brief sentences, this final challenge constituted a definitive proof of the human being’s inability to imitate the Qur’an. Can the person of today take up the challenge of the Qur’an and produce a Surah like it, thereby conquering the stronghold of Islam and invalidating the claim of its Prophet?

Let us not forget that this challenge was issued to a people whose leaders were threatened by the devastating attacks of the Qur’an – their lives, their property, their ancient customs, their ancestors, their whole social position. If it had been at all possible for the Arabs to respond to the challenge of the Qur’an, they would have taken it up immediately, with the unstinting aid of the masters of eloquence that were by no means rare in that age. Thus they would have invalidated the proofs of the Qur’an and won an everlasting victory.

Qur’an has proposed a very simple challenge to those who oppose it. Why do then the deniers of prophethood choose roundabout ways, avoiding this direct method of confronting and defeating Islam? Is not because the door is firmly closed on meeting the challenge posed by the Qur’an?

It is not that they did not try to mute the challenge. Infact, they called into play all their resources in an effort to meet the challenge of the Qur’an, but all their efforts came to naught. They were unable to point even to a single error or defect in the Qur’an, and were obliged to admit that its words were situated on a higher plane than the thought and speech of the human being.