Short answer
Muslims believe Islam, meaning submission to the One God, is the faith of every prophet from Adam onward. The final message began with Prophet Muhammad ﷺ in 610 CE, so Islam in its final form is more than 1,400 years old.
Sunni belief is that all prophets taught the same religion of tawhid (the oneness of Allah), called Islam, while their laws differed. The Quran was revealed to the Prophet ﷺ over 23 years, starting around 610 CE, and the Hijri calendar starts in 622 CE.
The four schools agree on this.
Explanation
There are two answers. Historically, the message of the Prophet Muhammad ﷺ began when the first revelation came in the cave of Hira, around 610 CE. He migrated to Madinah in 622 CE, which is year 1 of the Islamic calendar. So the Islamic calendar is now in its fifteenth century, and Islam as a community is over 1,400 years old.
In Islamic belief, though, Islam did not begin in the seventh century. The word means submission to Allah. The Quran calls Ibrahim "a Muslim", and says Allah ordained for us the religion He enjoined on Nuh, Ibrahim, Musa and Isa. Every prophet taught the worship of One God. The laws for prayer, food and so on changed from one prophet to another, but the core faith stayed the same.
The Prophet ﷺ compared himself to the last brick in a beautiful house built by the prophets before him. People admired the house but asked why one brick was missing. He said he was that brick, and the seal of the prophets. So Muslims see him not as the founder of a new religion but as the final messenger of the oldest one.
That is why Muslims love and believe in all the prophets. Read Stories of the Prophets, What Is Islam? and How many prophets are there in Islam?
The evidence
Quran, Surah Aal-i-Imraan 3:19
إِنَّ ٱلدِّينَ عِندَ ٱللَّهِ ٱلْإِسْلَٰمُ ۗ وَمَا ٱخْتَلَفَ ٱلَّذِينَ أُوتُوا۟ ٱلْكِتَٰبَ إِلَّا مِنۢ بَعْدِ مَا جَآءَهُمُ ٱلْعِلْمُ بَغْيًۢا بَيْنَهُمْ ۗ وَمَن يَكْفُرْ بِـَٔايَٰتِ ٱللَّهِ فَإِنَّ ٱللَّهَ سَرِيعُ ٱلْحِسَابِ ﴿١٩﴾
Indeed, the religion in the sight of Allah is Islam. And those who were given the Scripture did not differ except after knowledge had come to them - out of jealous animosity between themselves. And whoever disbelieves in the verses of Allah, then indeed, Allah is swift in [taking] account.
Islam is the one religion accepted by Allah.
Quran, Surah Aal-i-Imraan 3:67
مَا كَانَ إِبْرَٰهِيمُ يَهُودِيًّۭا وَلَا نَصْرَانِيًّۭا وَلَٰكِن كَانَ حَنِيفًۭا مُّسْلِمًۭا وَمَا كَانَ مِنَ ٱلْمُشْرِكِينَ ﴿٦٧﴾
Abraham was neither a Jew nor a Christian, but he was one inclining toward truth, a Muslim [submitting to Allah]. And he was not of the polytheists.
Ibrahim is called a Muslim.
Quran, Surah Ash-Shura 42:13
۞ شَرَعَ لَكُم مِّنَ ٱلدِّينِ مَا وَصَّىٰ بِهِۦ نُوحًۭا وَٱلَّذِىٓ أَوْحَيْنَآ إِلَيْكَ وَمَا وَصَّيْنَا بِهِۦٓ إِبْرَٰهِيمَ وَمُوسَىٰ وَعِيسَىٰٓ ۖ أَنْ أَقِيمُوا۟ ٱلدِّينَ وَلَا تَتَفَرَّقُوا۟ فِيهِ ۚ كَبُرَ عَلَى ٱلْمُشْرِكِينَ مَا تَدْعُوهُمْ إِلَيْهِ ۚ ٱللَّهُ يَجْتَبِىٓ إِلَيْهِ مَن يَشَآءُ وَيَهْدِىٓ إِلَيْهِ مَن يُنِيبُ ﴿١٣﴾
He has ordained for you of religion what He enjoined upon Noah and that which We have revealed to you, [O Muhammad], and what We enjoined upon Abraham and Moses and Jesus - to establish the religion and not be divided therein. Difficult for those who associate others with Allah is that to which you invite them. Allah chooses for Himself whom He wills and guides to Himself whoever turns back [to Him].
The same religion was given to all the great prophets.
Sahih al-Bukhari 3535
Sahih... مثلي ومثل الأنبياء من قبلي ...
"My example and the example of the prophets before me..."
He is the final brick in the house of prophethood.
Where the ruling is recorded
- Fath al-Bari (Ibn Hajar), Commentary on Kitab al-Manaqib, chapter on the seal of the prophets. Explains the parable of the house.
- al-Bidaya wa al-Nihaya (Ibn Kathir), Opening volumes on the creation and the stories of the prophets. Ibn Kathir presents history as one chain of prophets ending with Muhammad.
This answer is pending review by the scholars on our team. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.