What is the first congregation, is their prayer valid, and is it better to join them or to wait for the mosque's imam and his congregation?

It is not permissible to hold a congregational prayer in the mosque before the regular Imam's congregation, except with his permission or for a valid excuse, based on the Prophet's (peace be upon him) saying: "A man should not lead prayer in another man's domain."

If a congregation prays before their regular Imam without his permission or a valid excuse, there is a difference of opinion regarding the validity of their prayer. The more accurate view is that their prayer is valid, though they incur sin; because the prohibition relates to encroaching upon the Imam's authority, not to the essence of the prayer itself.

Therefore, it is not permissible to join them and pray with them if they establish the prayer before the regular Imam without his permission or a valid excuse. However, if the Imam is delayed beyond the usual time, there is no harm in one of them stepping forward to lead the people in prayer.