1.
Qur'an itself is not the proof. It's credibility as being the true source of Islam itself is questionable, as Muhammad didn't himself sit down and write it. Rather it's compiled together after the Prophet's death. It's the same issue that exists with Christians & their Bible. It's the same issue that exists with Buddhism. The only religions who bypass this issue out of the World's Major religions would be Sikhi & Hinduism, with the Vedas written by the ancient vedic people and the Granth being written by the teachers of Sikhi themselves. (Now this doesn't mean these two religions are more credible or w.e than Islam, but simply their scriptures have more credibility when pertaining to being a true source for their religion).
2. Hadiths themselves are a controversial issue, and not always in full-agreement with the Qur'an. Their very existence again makes the Qur'an less credible as being the source of Islam. Because if Qur'an is the word of God, there is no reason for a secondary text. Now this issue exists in other religions like Sikhi as well, where there are secondary texts that are considered of near same importance as the main text, despite there being contradictory points.
3. Sunnah, same issue as Hadiths. No written by Muhammad, but hearsay on what Muhammad potentially could've said.
"Predictions of the prophets".. the prediction arguments are really bad. Nearly every religions claims their founders made predictions which are now coming true. You have the Christians with the twin towers, and so on. Most of these predictions are simply based on people's interpretation of the texts or sayings.
Furthermore, Islam in northern India was in such a bad condition because Muslims while claiming to be Muslims, didn't actually follow the saying, and those who did followed the wrong ones.
Which is why in that specific region the founders of Sikhism (a controversial religion itself), Guru Nanak, started to comment on what a true Muslim should be:
1st. Because Muslims in power at that time were committing horrendous acts, he made the following comments on what a Muslim should be, because Muslims called themselves Muslims, but they really weren't Muslims (which is the same issue in the modern world):
"
There are five prayers and five times of day for prayer; the five have five names.
Let the first be truthfulness, the second honest living, and the third charity in the Name of God.
Let the fourth be good will to all, and the fifth the praise of the Lord.
Repeat the prayer of good deeds, and then, you may call yourself a Muslim.
O Nanak, the false obtain falsehood, and only falsehood."
"It is difficult to be called a Muslim; if one is truly a Muslim, then he may be called one.
First, let him savor the religion of the Prophet as sweet; then, let his pride of his possessions be scraped away.
Becoming a true Muslim, a disciple of the faith of Mohammed, let him put aside the delusion of death and life.
As he submits to God's Will, and surrenders to the Creator, he is rid of selfishness and conceit.
And when, O Nanak, he is merciful to all beings, only then shall he be called a Muslim."
2nd. The acts committed by Muslims of the late 1400s under Babur who invaded Northern india at time, genociding Hindus and even other muslims in the name of Islam. Led Nanak to write this:
"
Since Babar's rule has been proclaimed, even the princes have no food to eat. || 5 || The Muslims have lost their five times of daily prayer, and the Hindus have lost their worship as well. Without their sacred squares, how shall the Hindu women bathe and apply the frontal marks to their foreheads? They never remembered their Lord as Raam, and now they cannot even chant Khudaa-i || 6 || Some have returned to their homes, and meeting their relatives, they ask about their safety. For some, it is pre-ordained that they shall sit and cry out in pain. Whatever pleases Him, comes to pass. O Nanak, what is the fate of mankind? || 7 || 11 ||"
Even in the late 1300s, Islam's "heads" had reached high level of corruption and thus a poet of that time wrote this:
"
You keep your fasts to please Allah, while you murder other beings for pleasure.
You look after your own interests, and so not see the interests of others. What good is your word?
O Qazi, the One Lord is within you, but you do not behold Him by thought or contemplation.
You do not care for others, you are a religious fanatic, and your life is of no account at all.
Your holy scriptures say that Allah is True, and that he is neither male nor female.
But you gain nothing by reading and studying, O mad-man, if you do not gain the understanding in your heart.
Allah is hidden in every heart; reflect upon this in your mind.
The One Lord is within both Hindu and Muslim; Kabeer proclaims this out loud. "
Genocides, rapes, destruction of villages & cities has happened under the name of "Muslim" & "Islam". Throughout history Muslims & Islam in various regions has been criticized. The reason it couldn't in the middle east is because of the Kingdom's at various times practiced a hardcore militarism when it came to implementing Islam in the culture of the religion.
Now you might be saying why I'm giving you this short history lesson and it's relevance to your post on "proof". Well the reason it's mentioned is because you said Islam is a religion of proof. So when did this "proof" show up?? Because it certainly did not exist in those eras, where heinous acts were being committed under the name of Islam, where scriptures such as the Quran itself was used to justify those heinous acts. The ones who committed such acts also had high-level scholars under them who knew the language of the Quran much better than any modern individual today, as well had more information on the era and the situation the religion was formed in.
So no my friend you do not have any "proof", what you have is simply your perception of having "proof". People follow buddhism due to it's ideologies. People follow Hinduism due to semi-practicalities of the vedic people who combined science/religion. People follow Judaism & Christianity for some of the good things/morals that exist in them. People follow Sikhism for the samething as the rest. The reason people follow other religions goes beyond just "belief". People claim their religion tells the right way with "proof", but really none do. Yes nearly all religions have some aspects and teachings that are universal and based in reality. Like Buddhism's meditation ways which do help the physical body and mind. The stories of the bible that can be used to teach people some basic "morals".
As for why people follow Islam. Islam was forced upon millions of people across Middle East & Asia throughout it's history. No different than Christianity in Europe and Americas. No different than Hinduism in India. Thanks to the various empires/kingdoms that adopted those religions. Now a lot of people are well engrossed into those religions due to their cultures/families/being raised that way, that people now spread them to others. Then of course there is religious propaganda where people use wrong information regarding other religions to make theirs look better ( Dr. Naik is well famous for that for Islam).