Modern Muslims didn't meet Muhammad, nor did modern Christians meet Jesus Christ. You can go on and mention all followers of all old religions and beliefs. There is no way to meet Jesus and ask him whether he was divine (according to Christian belief) or just a human messenger from God (according to Muslim belief). Prophets and messengers came with miracles that only those who have seen them could witness. Those miracles are useless as a proof for all of us who were not there. And there comes the meaning of what Islamic scholars say: the only forever valid miracle of Islam and of Muhammad is the Book; the Quran.
Today I will not go into any details other than an artistic one. I love music. But if you go into any mosque (place of worship of Muslims) you will not find any musical instrument, and you will never find one in the near or the far future. In a mosque, we can get our music from the recitation of the Quran. See the video below as an example of the music of the Quran. The language of the Book is so unique and special, and it's very common among Muslims to see people who memorize the whole Quran by heart since a very young age. It is certainly the only book of its size that is known by heart by millions all over the world. This is explained in the Quran itself, where God says that He made it easy to be read and recited. Beauty makes things easier and more accessible. I myself see any truth as inseparable from being beautiful!
"And certainly We have made the Quran easy for remembrance, but is there anyone who will mind?"