What proof a Muslim can give to a non muslim that the book that is available today is the same as what was revealed to Holy Prophet PBUH, without any alternation?
Simple answer: Most of the words can be considered authentic. The order and wording may not be the exact same in all places.
Long answer: Muslim means "someone in a state of peace". According to the Quranic manuscripts we have today, a muslim holds faith in one God and is steadfast in the daily prayers towards God. In other words a person in a state of peace follows the religion of Abraham whose narrative known at the time of Muhammad is found mostly in the book of Genesis in the Torah if not the Quran itself.
Therefore a non-muslim, is someone who has no faith in God or that, in practice holds faith for several gods: worldly idols of any nature, past or present.
Having faith in one God or not is independant to whether you might think the quranic text is "altered". Quran was a spoken word that conveyed a message: do good and forbid evil, get a grasp of the real world, get sensible with regards to life, find the middle way and get muslim.
There used to be many written versions of the Quran. It was then standardized by one of the first four caliphs succeeding Muhammad and all other copies were disposed of. The standardization was eventually accepted by both shias and sunnis and gave us the quran we have today although even today some qurans have different harakat than others which in some sense is alteration. One of the oldest manuscripts of the quran we have today shows signs of reordering of verses and changing words. The main message and corpus however remains the same, only circa 100 years after the death of the prophet.
Truth cannot be altered, truth always prevails and any truthful words that have been put into writing cannot be altered in the sense that they will never become a lie. From the quran we have today, take the good.
The real answer: Allahu 3alem. God is most knowing.
There are lots of proves about It,I try to note some of important proves:
1.Quranic verses and Allah promise about Quran Preservation:
"Indeed, it is We who sent down the Qur'an and indeed, We will be its guardian."(Surat Al-Ĥijr,verse9)
"Indeed, upon Us is its collection [in your heart] and [to make possible] its recitation."(Surat Al-Qiyāmah,verse17)
2.Challenge verses in Quran:
"And if you are in doubt about what We have sent down upon Our Servant [Muhammad], then produce a surah the like thereof and call upon your witnesses other than Allah , if you should be truthful."(Surat Al-Baqarah,verse23)
this verse always exists in Quran which mention 2 points:
a.if Quran has been changed,this verse would be deleted but It always exists.
b.nobody can change text of Quran because of its eloquence and rhetoric.
3.similarity and resemblance of all Lineal Qurans all over the world. all ancient Versions of Quran which exist in different old museums in different countries are the same which shows Lack of distortion of Quran. because It is impossible that all people all over the world change Quran same as each others.
4.Quran wasn't specific for specific group.so if one group wants to change it,other groups will decry it.
5.Hadithe Thaqalayn which all Muslims Have accepted it,mentions another reason.Distortion of Quran will destroy validity of this hadith.
6.Consensus of all Shiite and Sunni Scholars of Islam about lack of distortion.
7.miracle of Quran.
reference in persian :http://shamimshia.com/fa/esbat-haghniat-ghoran/223-esbat-adam-tahref
No need to prove it, you cannot find one mistake or contradiction or scientific error in it, not only that but a simple challenge if we must prove it's originality, we will say it's not the same if you can even produce one simple ayat (verse) like it, that has the same beautiful poetry and scientific essence to it as the holy Quran.