Answered by Shaykh Gibril F Haddad
The answer is threefold:
1. In the cosmic sense Islam began with creation as all things great and small surrender to the Creator;
2. In the sense of a Prophetic dispensation Islam began with Adam, upon our Prophet and upon him blessings and peace, since Adam was taught what the angels knew not and was thenceforth their teacher;
3. And in the historical sense it began 1437 years ago, when the Prophet Muhammad (peace and blessings be upon him) was appointed with his messengership.