The speed of the conquests is the hardest fact of the period to absorb. Within twenty years of the Prophet's death, armies from Arabia had taken Syria after the Yarmuk in 636, Iraq after Qadisiyya, Jerusalem in 638, Egypt by 642 and the Persian heartland by the early 650s, against two empires that had just exhausted each other in a generation of war. Conquest did not mean conversion. The armies were settled in new garrison cities, Kufa, Basra and Fustat, deliberately apart from the populations they governed, and the great majority of those populations remained Christian, Jewish or Zoroastrian for centuries.
The legal shape of that arrangement is the dhimma, the protected status of scriptural communities, who kept their own law, courts and worship in exchange for a tax and for accepting subordination. Milka Levy-Rubin's work shows that the terms were originally negotiated locally at surrender and were far less uniform than the later law books suggest, and that the restrictive conditions attached to the status hardened considerably after the first century.
The caliph himself was not a prophet and made no claim to revelation. He led prayer, commanded the armies, appointed governors and judges, and distributed the conquest revenue; the definition of doctrine was not among his powers, and the failure of a later caliph to seize it would settle the point permanently.