Is the Prophet's not having done a religious matter, or the first three generations' not having done it, considered sufficient evidence to declare every innovated matter an innovation (bid‘ah), such as the Mawlid (Prophet's Birthday) celebration, taking into account that not doing something does not necessarily imply a prohibition, and that some of the Salaf (early Muslims) performed acts that were not specifically mentioned?

Innovation (Bid'ah) is that which Allah and His Messenger did not legislate, nor command, whether as an obligation or a recommendation, and which the Prophet (peace be upon him) and his Companions did not do, nor does it fall under a legal principle.

Examples of what the Prophet (peace be upon him) left due to an impediment, then it was done after him and was not an innovation: 1. Performing Tahajjud in congregation: The Prophet (peace be upon him) did this during the last ten nights of Ramadan for some nights. Umar ibn al-Khattab (may Allah be pleased with him) gathered people for Tarawih prayer and called it a linguistic innovation because the Prophet (peace be upon him) left it out of fear that it might become obligatory for them. 2. Actions that did not exist during his time but occurred afterward, such as modern developments or matters like the compilation of the Qur'an and the codification of Islamic laws, were not innovations.

An example of what the Prophet (peace be upon him) left despite the presence of the reason for it and the absence of any impediment, so doing it would be an innovation: 1. Celebrating his birthday (peace be upon him); because the reason for it was present during his era and the era of the Companions, yet they left it. Therefore, doing it is considered an innovation.

The Prophet's leaving something could be a Sunnah, and doing it afterward would be an innovation, if the reason for the action was present during the Prophet's time and the impediment was removed, yet he still left it, such as leaving the adhan for the two Eids.

As for the action of Sheikh al-Islam Ibn Taymiyyah (may Allah have mercy on him) of frequenting abandoned mosques and rubbing his face in the dirt while supplicating to his Lord, this is not an innovation, because worshipping Allah in mosques, avoiding people, seeking solitude, and prostrating and humbling oneself to Allah in supplication are all matters indicated by the Islamic law.