Bukhari

Hadith Commentary:

If it is in His knowledge that, upon reaching maturity, they would have been doers of good deeds, then they will enter Paradise; otherwise, Hell.

Apparently, this hadith is problematic, because whatever is in His knowledge necessarily comes to pass. So, in His knowledge, it was that they would die in childhood.

The answer to this objection is that the definitive matter was indeed that they would die in childhood, and the Lord certainly had knowledge of this. However, along with this, the Lord also knew that if they had lived, they would have been fortunate (righteous) or unfortunate (wicked).

And knowledge is with Allah.

Hadith Commentary:
(1)
From this heading, it is understood that Imam Bukhari rahimahullah was initially undecided regarding the children of the polytheists, but afterwards he became certain about their salvation.
From these hadiths, it is understood that Allah, the Exalted, will deal with them according to His knowledge.
This is also the position of Imam Ahmad and most of the scholars, that since these children are, according to the Shariah, not legally responsible (ghayr mukallaf), their matter should be left to Allah, because He knows best whether they are deserving of Paradise or worthy of Hellfire.
If, in His knowledge, they would have performed good deeds had they grown up, then they will enter Paradise; otherwise, they will become fuel for Hellfire.

(2)
The Qadariyyah (a deviant sect)
say that in this hadith, salvation or lack thereof is made dependent on actions, and children are born upon the natural disposition (fitrah) of Islam, so since they have not committed shirk at all, they are necessarily deserving of salvation. However, this interpretation is not correct, because after being born upon the fitrah, if they were given life, what would they have done? Allah, the Exalted, will decide regarding their potential life based on His knowledge, and He is fully aware of it.
Thus, this hadith is evidence that Allah, the Exalted, has knowledge of a person’s possible future life and their deeds which have not yet occurred.

(3)
Hafiz Ibn Hajar rahimahullah has written that on the Day of Resurrection, the people of the interval (Ahl al-Fatrah) and the insane will be tested.
It will be said to them: “Throw yourselves into the Hellfire.”
Whoever, in obedience to Allah, jumps into the Hellfire, for him it will become cool and peaceful, and whoever refuses to jump into the Hellfire will be handed over to the Fire.
(Fath al-Bari: 3/313)
It is possible that in the Plain of Gathering (Mahshar), some test of action may also be prescribed for the children, upon which their salvation or destruction will depend.
And Allah knows best.

Hadith Commentary: Benefits and Issues: According to Ahl al-Sunnah, Allah has knowledge of (ma kana) (what has occurred), (ma yakun) (what will occur), (ma la yakun) (what will not occur), and (law kana kayfa kana yakun), that is, if it were to occur, how it would occur—He has knowledge of all these.

1951. Commentary: That is, Allah the Exalted will judge according to His knowledge. In view of such ahadith, some scholars advocate silence and suspension of judgment regarding this issue.

Takhrij:
[صحيح بخاري 1384],
[صحيح مسلم 6765]

Fiqh al-Hadith:
➊ Will the children of the polytheists enter Paradise or Hell? This is an issue of predestination (qadar); only Allah knows what deeds they would have performed in the world.
➋ The funeral prayer (salat al-janazah) is not to be performed for the children of the polytheists.
➌ It is better to remain silent regarding the children of the polytheists.
➍ Also see: [اضواء المصابيح : 84، ماهنامه الحديث حضرو : 33 ص6]