Will the baby be sentenced to hell since s/he didn't have a chance to choose Jesus before death?
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I think the bible doesn't explain this question, so I can't answer on my own because we can't add or take out anything from the book.
That's a very good point. We can theorize, but the Bible does not go into any real detail on this matter. The closest, perhaps, is David's statement about his son that "I will go to him" - but even this is not clear as to whether David is meaning he will see His son resurrected, or merely that he will one day die and go to the grave as his son did, but his son will not return to the land of the living.
'Even so it is not the will of your Father which is in heaven, that one of these little ones should perish' - Matthew 18:14
God is our creator and He is their's too. I believe with all my heart that they have a soul which He also gave them. They are His and when their body dies their soul returns to Him. I believe that they will be there in Heaven where we will see them when we go there. They are innocent of all but original sin and they did not have the chance to grow to the age of accountability at which time they could purposefully sin or ask for forgiveness from sin (original or otherwise).