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 is His slave and Messenger.
If a little boy who has started to learn how to speak sneezes, then he should be taught, and one may say to him, for example, “Say: ‘Alhamdulillah’ (Praise be to Allah);” but if he does not yet discern what he is taught and does not speak properly, then there is no harm in praising Allah on his behalf or ask Allah to bless him, and the like.
However, one should not intend that this is a confirmed Sunnah from the Prophet ; this is just to mention Allah and supplicate Him. So one supplicates for him because this was reported from some righteous predecessors; Ibn Muflih said in Al-Aadaab Ash-Shar’iyyah, “Abdullah ibn Ahmad narrated from Al-Hasan that he was asked about a young boy who sneezes, and he said, ‘One should say to him, 'Boorika feek' (i.e. May you be blessed).’”
If a person keeps silent and does not say anything to him and does not praise Allah on his behalf, then there is nothing wrong with this because the pen is lifted from the child and he is not required to do anything; so the matter is easy, Allah willing.
It is recommended that the boy hears good words, such as saying ‘Alhamdulillah’ (praise be to Allah), ‘Subhaan Allah’ (Glory be to Allah), and so forth, so that the child becomes accustomed to this even if he has not started to speak yet, and it is recommended that this is the first thing that he hears at birth.
At-Tirmithi, Abu Daawood and others reported that “the Prophet recited the athaan in the ear of Al-Hasan ibn 'Ali when he was born to Faatimah.”
Therefore, there is no harm that he hears ‘Alhamdulillah’ and supplications.
Allah knows best.