This absence of evidence has led some historians to speculate that the Arab armies weren't Muslim at all- that they were on a conquering mission, not a religious one- and it was only later, once they'd got their feet under the table, that they saw the need for an new, distinctive ideology to validate their empire and prop it up. That's when they discovered they'd once had a prophet of their own. As for Mohammed himself, internal evidence suggests he composed the Koran in a fertile area close to the Dead Sea, a long way away from Mecca. His mythos got itself relocated there because (for chauvinistic reasons) the Arabs needed to associate him with their heartland.
If you'd like to experience this material cut with a lot of entertaining ancient history read Tom Holland's book In The Shadow of the Sword; some critics have compared it to Gibbon. If you have 95 minutes to spare you might want to watch the TV film in which the same material is cut with a lot of footage of Holland wandering round the Middle East looking haunted.