What is the ruling on the "noon party" that is held when a child's first tooth appears, and what are the permissible celebrations for children?

The default ruling is the permissibility of celebrating joyous worldly occasions such as the birth of a child, success, or the return of a traveler, provided that these celebrations do not involve imitating disbelievers and are not taken as recurring annual festivals. This is based on the Prophet's (peace be upon him) saying: "Whoever imitates a people is one of them," and his saying: "Indeed, Allah has replaced them for you with two better days: Eid al-Adha and Eid al-Fitr." Ibn Uthaymeen issued a fatwa (definition) permitting celebrations to show joy and happiness, not as an act of worship, provided there is no extravagance and that they are not considered a recurring 'Eid if they do not repeat annually. Therefore, there is no harm in celebrating the emergence of a child's first tooth, their first steps, or their first words, provided the celebration is not repeated every year.