Depends on how you define "original sin."
To me, original sin simply means that we have inherited the same weaknesses that led to Adam and Eve's first sin, and that those weaknesses cause us to sin as well. However, I believe that total depravity can only be supported by taking Scripture out of context and using a very literal interpretation. Many who believe this theory will point to Jeremiah 17:9 ("The heart is deceitful above all things and desperately wicked"), but I don't think that people sin because their hearts are wicked; rather, their hearts are wicked because they sin. When Genesis 8:21 says that "everything they think or imagine is bent toward evil from childhood," it is referring to the people that God destroyed in the flood, not necessarily humanity for all time (see Genesis 6:5). And when David says that he was conceived and born in sin, he is using a poetic device.
That being said, the Bible does say that we are all sinners, and it clearly suggests that there is an age of accountability. The belief in baptizing babies and small children is based on the concepts of original sin and total depravity, but they are not held accountable for any sins they commit in their lives until they are old enough to understand and recognize that they have sinned. I guess you could say that that is when someone "falls into sin": when they realize that they are sinners and need God's grace for salvation.
Some interesting articles on the subject of original sin and total depravity:
http://www.tillhecomes.org/jeremiah-17_9-total-depravity/https://www.christiancourier.com/articles/276-original-sin-and-a-misapplied-passagehttp://www.tillhecomes.org/genesis-6_5-genesis-8_21-total-depravity/http://www.tillhecomes.org/only-evil-continually-calvinism-genesis-6_5/
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