I asked my Italian professor (a native speaker) a while after posting this. She says "fin da" and "da" are a little different. "fin da" marks a fixed point or limit. It's a bit less general than just "da". I think "da" is like "since" and "fin da" is more like "ever since".

Incidentally, "fin" and "sin" are interchangeable. You should use the one that sounds better.