The Morello family is widely considered to be the first Family but how true that is I don't know. But if you believe that scenario then you could make the assumption that Morello was the first.

I've also heard the Mafia in the US originated in New Orleans which would dispute Morello and his family being the first.

I think in Al D'Arco's book, he claims the first Mafia family originated in New Jersey and has a direct line to the modern day Lucchese family. So who the first was may be a question we never get an answer to.

I don't think any credit goes to the Terranova brothers as being the first because although they were Morello's step brothers they were much younger than he was. They pretty much followed in his foot steps and didn't take over the Morello family until Giuseppe the clutch hand was imprisoned in I believe 1910 or so.