Is it permissible to say "may Allah have mercy on them" (tarahhum) for the children of disbelievers who died before reaching the age of puberty?

Scholars hold different views regarding the children of polytheists. Some believe they are in Hell, following their parents. Others withhold judgment concerning them. Still others are of the opinion that they are among the people of Paradise, citing as evidence what Al-Bukhari narrated about the Prophet, peace and blessings be upon him, seeing Abraham, peace be upon him, in Paradise surrounded by the children of people and polytheists, and also by Allah Almighty's saying: "And never would We punish until We have sent a messenger." [Al-Isra: 15].

The soundest of opinions is what the Prophet, peace and blessings be upon him, said when asked about them: "Allah knows best what they would have done," narrated by Muslim, meaning what they would have done had they reached maturity. Sheikh al-Islam Ibn Taymiyyah mentioned a hadith indicating that they will be tested on the Day of Resurrection, and whoever obeys will enter Paradise, and whoever disobeys will enter Hell, and they will be recompensed for what appears from them of faith or disbelief.

Therefore, it is not permissible to seek forgiveness for them, because seeking forgiveness is not permissible for non-believers, and nothing has been transmitted from the Companions and Successors indicating its permissibility.