Praise be to Allah.
If what you mean by the “Muslim tradition” is the Islamic religion itself, the answer will be given in the second section below.
1-But if what you mean is what the Muslim ummah (nation) has achieved down throughout the ages of prosperity, then this was not achieved in one instant, but it started when Islam started, especially after the establishment of the Islamic state at the time of the Prophet (peace and blessings of Allaah be upon him), then it started to flourish and develop as the Islamic conquests spread and reached the level that they did. If this can be attributed to anyone, it can only be attributed to the Prophet (peace and blessings of Allaah be upon him), after Allaah. With regard to other people, everyone contributed as much as he could until the structure (of the Muslim civilization) was complete.
2-With regard to the beginning of the religion, it seems that what is meant by religion is the religion of Islam with its beliefs and laws. This started with the mission of the Prophet (peace and blessings of Allaah be upon him).
With regard to the rules of Islam, they are many and it is difficult to list them all here, but the most important of them are:
The testimony that there is no god except Allaah and that Muhammad is the Messenger of Allaah; establishing regular prayer; paying the zakaah (obligatory charity, a share of one’s wealth to be given to the poor); fasting in Ramadaan; and Hajj or pilgrimage to the Sacred House of Allaah.
An individual enters this religion after bearing witness that there is no god except Allaah and that Muhammad is the Messenger of Allaah, then after that he is obliged to adhere to the other pillars, prayer, fasting and Hajj. There are many further details involved in these matters.
See also Question # 13569