As I understand it these are the only facts known:
There is only one brief mention of a man called Mohammed in any contemporary historical document.
In the Arabic coinage of the time there are no coins depicting Mohammed.
In the Arabic coinage of the time and until much later there are no coins with quotations from the Koran.
The earliest known mosques are not in Medina or Mecca they are in present day Syria.
In the earliest mosques there are no quotations from the Koran as we now know it.
The inscriptions that are there were altered much later to conform to the present text.
Islam probably did not originate in Medina and Mecca but in Syria
which was far more advanced culturally
and had much greater contact with Judaic and Christian ideas.
I am not a historian so I cannot provide references.
However I shall endeavour to do this if you are interested.
None of which addresses the religious and political movement involved. Religions are not books, nor are they based on books in their formative periods. Books are means to preserve traditions that already exist, not the origin of new ones. Remember that only a tiny minority of the ancient world was literate in any way, and most writing there was, was restricted to practical matters of rule or commerce. With priestly matters a third, in more civilized areas.
The salient political fact is that both Syria and Egypt were conquered by Arab armies commanded by one caliph Omar, who ruled as successor ("caliph") to an Arabian monotheist prophet named Muhammad, who had already consolidated the support of most of Arabia before Omar took power. This is not any made up tradition, but a massive historical fact clearly seen in the history of the rival empires of the area, Persia and Byzantium.
Omar's political and military system was legitimated by claiming to follow the previous practices of Muhammad, down to the portions of division of spoils, tax laws, who owed military service, and conditions of surrenders. When an area was conquered, those who converted became soldiers in the new regime, those who did not owed tax. "The Muslims" and "the army" were synonomous. They lived seperated in military encampments, under a sort of military-religious discipline.
Some time later, after further military successes, a succession crisis split the force. When the dust cleared, a different family dynasty, headed by the governor of Syria under the previous ruling group, a family that was originally from Mecca but were rivals even there of the previous ruling house, was in charge of the regime. The court moved to Damascus. Seperatist movements remained in existence, though their size and influence is hardly known.
Under the new dynasty, the Omayyads, the whole thing settled down. Soldiers were settled on land in return for owing taxes. A "civil list" supported by taxes grew up. The strict regimentation of the previous period relaxed. And men began writing down - or making up - traditions about the earlier period, and about the actions of Muhammad, to justify whatever they wanted done. With the nearby power of both Bzyantium and Persia already broken, the new regime continued to expand, incorporating all of Persia and most of North Africa, and making inroads into Asia minor. Frontiers and central court were differentiated. Taxes flowing in to the court in Damascus funded construction, art, and literature in a serious way, for the first time in the movement's history.
Less than a century later, the Omayyad dynasty fell apart, in turn. Opposition movements formed around the changes in taxation, resentment of the civil list as producing inequality, disputes over division of spoils, theological controversy as factions fought over their "traditions" and absorbed hellenist, christian, and persian influences. The army shifted from all Arab to mixed Arab and frontier recruits, particularly from Persia. A new dynasty largely backed by the Persian faction of the army overthrew the Omayyads and moved the capital to Baghdad. There it stayed for hundreds of years.
This is the sort of standard history you get from British turn of the century orientalists like Duncan McDonald. There is zero credulity toward Arab legend spinning involved in any of it. Do not confuse Arab legends about the Koran (tremendously falsified for doctrinal reasons) and about Muhammad's particular actions, sayings, and rulings (falsified in detail to support this or that principle or faction), with the basic political history of the movement's formation and political spread. The last is quite well known.
I did find that the Catholic Encyclopedia entry on Mohammed says:
The sources of Mohammed's biography are numerous, but on the whole untrustworthy, being crowded with fictitious details, legends, and stories. None of his biographies were compiled during his lifetime, and the earliest was written a century and a half after his death. The Koran is perhaps the only reliable source for the leading events in his career. His earliest and chief biographers are Ibn Ishaq (A.H. 151=A.D. 768), Wakidi (207=822), Ibn Hisham (213=828), Ibn Sa'd (230=845), Tirmidhi (279=892), Tabari (310-929), the "Lives of the Companions of Mohammed", the numerous Koranic commentators [especially Tabari, quoted above, Zamakhshari 538=1144), and Baidawi (691=1292)], the "Musnad", or collection of traditions of Ahmad ibn Hanbal (241=855), the collections of Bokhari (256=870), the "Isabah", or "Dictionary of Persons who knew Mohammed", by Ibn Hajar, etc. All these collections and biographies are based on the so-called Hadiths, or "traditions", the historical value of which is more than doubtful.
These traditions, in fact, represent a gradual, and more or less artificial, legendary development, rather than supplementary historical information....
If the accepted story of Mohammed's life was simply developed over time as a legend in service of furthering Islam, it shines a different light on events such as Mohammed's massacre of the Jews in Yathrib (before it was renamed Medina, the City of the Prophet), or his marriage to the six-year old girl Aisha, consummated when she was nine. If his life is a created legend, did the early Muslims think that these stories would illustrate the holiness of Mohammed's character?