According to the Catholic Catechism, every spiritual soul is directly created by God. At the moment the individual is created by God, does it have original sin? Or is original sin added later?
You touch on one of the great difficulties that Christians have wrestled with for the entirety of Christian history. I agree with the above comments that your question could benefit from being a little more tightly focused. I will answer the first part about original sin, leaving aside for now the questions about predestination and free will. I have no shame in shying away from those topics or admitting that I'm hesitant/unqualified to deal with them.
From a Reformed perspective (you didn't specify a particular doctrinal tradition so I will answer from the one I know and adhere to), we are under the curse of original sin from the moment of conception. I would point to Psalm 51, where David says that he was "conceived in iniquity", and to Ephesians 2, where Paul refers to us as being "by nature the children of wrath".
When Adam, as the federal head of humanity, sinned, all mankind fell at that moment. (See Romans 5.) Since then, all mankind save Christ has been born in sin, with a corrupted nature inclined toward rebellion against God. This is certainly not an easy thing to grasp, and I do intend to defer on the questions it raises regarding the justice of God because I don't feel I can adequately address matters of such weighty import here. If you are more interested in the Reformed perspective, I might recommend first reading through the book of Romans, in its entirety, at least 2 or 3 times. Subsequently, you might find a Protestant study Bible or commentary on the book of Romans. I could recommend the ESV Study Bible or the Reformation Study Bible, both of which will give you a good but succinct overview of the Reformed teaching on original sin - what it is and why we believe that it makes sense.
For a Roman Catholic perspective, you might check out para. 385-409 of the CCC, and the Confessions of St. Augustine (the latter being a source that Protestants would also readily affirm). However, I'm not Roman Catholic, so another person would be better qualified to inform you on that perspective.