The Islamic belief began in the 7th century with Muhammad. Muhammad was born in 570 and until he was 40 he led a regular life, he was married and worked as a trader. At 40 Muhammad experienced a divine revelation while meditating in a cave outside Mecca, around 610. He began to preach to family and friends and eventually the general public.
Muhammad believed that he was chosen by God to preach repentance, submission to God and the coming judgement day.
In 622 Muhammad and his many growing following fled to Medina, and this is considered the first year of his religious leadership. This is the year that the Muslim calendar began so it could be considered the official start of the religion.
It should be noted that Muhammad did not claim to be the leader of a new religion. He said he was reviving and old and pure tradition that he believed that Christians and Jewish fell away from.
So Islam is almost 1400 years old.
Here is a chronology of the faith.
http://www.usc.edu/dept/MSA/history/chronology/
