All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
It is permissible for children to touch the Quran and open it provided that they have reached the age of distinction and it is known that they would not touch it with a part of their body that is stained with impurity.
An-Nawawi wrote, “If the child has not reached the age of distinction, it is impermissible for his guardian to allow him to touch the Quran so that he would not violate its sanctity. If the child is discerning, the question arises as to whether the guardian or tutor should oblige him to purify himself before touching or carrying the Quran. There are two famous views in this regard; the most likely correct view according to the Shaafi‘is is that it is not obligatory given the hardship involved.” [Al-Majmoo’]
Allah knows best.