1- Prophet Muhammad ﷺ had no reason to lie, for 23 years straight, and gained no worldly benefit from what he taught. He was persecuted by the Makkans for years and he lived in poverty and hunger. The previous messengers, Jesus, Moses, and others(peace be upon them), also had no reason to lie. Prophet Muhammad ﷺ was known as al-Amin, the trustworthy, even before the message of Islam came. All historical narratives support this.
Literally there are only two options in this situation, either he and Jesus (peace be upon him) were telling the truth or he and Jesus(peace be upon him) were crazy, and crazy is beyond easy to rule out.
Claim: Prophet Muhammad's (ﷺ) message is believable and he was not lying because he had no purpose to lie.
Evidence: Humans have a reason behind everything that they do. Prophet Muhammad ﷺ gained no selfish benefit from what he taught.
Warrant: Humans only lie for a purpose. This purpose is always selfish gain, in one way or another.
Most common counterarguments:
He was deluded: This would mean he was mentally ill. There is no logical evidence to indicate this was the case at all. His behaviour was completely normal as recorded in all historical narratives.
He was not lying but mistaken: This is simply illogical, there would be no logical explanation for him believing Islam and being revealed it but being mistaken. There is nothing to cause this.
2- All other religions and belief systems have contradictions or things seriously wrong with them. But there are no contradictions in the Quran. It is the only religion without logical errors.
4:82(translation)
Then do they not reflect upon the Qur'an? If it had been from [any] other than Allah, they would have found within it much contradiction.
This is logical evidence that its claims are more valid than those of other religions, which all have contradictions/logical errors.
3-The existence of jinn, people worshiping them, and their behaviour, are big proofs. On observation of jinn and the religions that follow them, it can clearly be seen that these are the jinn that Allah has created. The jinn are spirits that generally belong to the unseen world, but some people communicate with them and worship them.
If you don't believe that an invisible world exists yet, consider this: We don't know anything about the nature of what was before the Big Bang, and we understand very little of quantum particle behaviour. Whatever was before the Big Bang was supernatural. Quantum physics that doesn't act according to physics is supernatural. The supernatural has been scientifically proven to exist. And magic and Jinn exist but cannot be explained by science.
4-The Jews and Christians knew that a prophet was to come. This is shown in the stories of Addas, Abdullah ibn Salman, Waraqa ibn Nawfal, Salman al-Farisi, and more. A lot of proof that refutes Christianity and Judaism supports Islam at the same time, such as the gospel of Barnabas, the Dead Sea Scrolls, and the controversy over the two gospels.
Evidence that could be considered subjective by some but in my opinion is true:
5-The content of the Quran itself. We judge what we read based on our previous beliefs. This is not something illogical to do, it is natural. When we read the Quran, we can clearly see that it is not an average religious book, based on our normally accepted beliefs. Based on my previous schemas, knowledge of language, knowledge of human behaviour, etc, when I read Quran, I honestly cannot believe that a human could have written it. And it is so melodic while making perfect sense at the same time.
Surah al-Rahman
https://www.youtube.com/watch?v=e0rU1lUhzjY
6- Islam is not self-serving. It does not benefit any leader or Imam. It solely benefits the one who follows it(when they follow it properly), giving them abilities like being able to avoid addiction, having a constant sense of peace, having a believable, real God to turn to in times of distress, not feeling overly attached to things, not being held back by false superstitions or false scientific beliefs, being naturally honest, knowing that knowledge is very important thus pursuing knowledge, having 1.5 billion sisters and brothers who love you without ever meeting you and who you can trust because you know they will(most often) never lie, always doing good for others, and other Muslims do good for you, and getting to go to Paradise.
This is evidence that gives support to Islam as a religion that benefits only the worshipper, because its purpose is not benefiting someone else’s exploitative purpose.
7- The fact that an experiment can be done to prove Islam is true. This is the experiment: Sincerely repent to Allah from all of your sins, and accept Islam. Because you are now sinless, your mind should automatically start believing Islam because the truth is not hidden except from people who have committed evil sins and follow Satan. Sins are a reason for being deprived of knowledge.
Here is another experiment: It can be proved that Satan is whispering to you when you have doubts by making dua that Allah removes your doubts, repenting sincerely, and asking Allah to help you. Also, examining your doubt carefully and seeing where it comes from and whether it fits the facts helps too. It must be remembered during this experiment that repentance should be sincere(there are three conditions to sincere repentance).
14:27(translation)
Allah keeps firm those who believe, with the firm word, in worldly life and in the Hereafter. And Allah sends astray the wrongdoers. And Allah does what He wills.
From 42:13(translation)
"....Allah chooses for Himself whom He wills and guides to Himself whoever turns back [to Him]."
13:27(translation)
And those who disbelieved say, "Why has a sign not been sent down to him from his Lord?" Say, [O Muhammad], "Indeed, Allah leaves astray whom He wills and guides to Himself whoever turns back [to Him] -
8-The evidence from other religions, which validate Islam's claims. For example, many polytheistic religions follow Satan and worship Jinn, which is spoken of in the Quran. Christianity and Judaism have been proven to have changed from their original teachings, which is also spoken of in the Quran.
9-The fact that some people can't accept Islam despite seeing proof is evidence in itself. We are told that many people will be misguided as a result of their evil actions.
10-The essence of the call. The main point of Islam is literally just to worship one God, the creator of the universe, and obey his command to worship him. It is simple and makes sense to everyone.Arguably, it makes the most sense out of all belief systems.
11-The Quran contains a way to prove that it is from a non-human source, it dares humans to create a surah like one of its surahs. This has been attempted but has never succeeded.
2:23(translation)
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.
17:88(translation)
Say, "If mankind and the jinn gathered in order to produce the like of this Qur'an, they could not produce the like of it, even if they were to each other assistants."