I am not sure if I was supposed to be allowed to do this or not but at the very beginning of the game, emerging from Vault 101, I head off towards Smith Casey's Garage in lieu of stopping by Megaton. Once I make it to Smith Casey's Garage, after multiple deaths and and frustration of being a level 1 in the out-and-about parts of the map, I gain access to Vault 112 and secure a seat in Tranquility Lane. Upon finishing Tranquility Lane I find Dad and we reunite and damn does it feel good. Then, it gives me the notification that I have completed the quest for that part of the story despite having done no other part besides escaping Vault 101.

Is this supposed to be able to happen? Or did I break the game?

I'm sure it's nothing urgently important but I've been curious about this, though.

Yup, it was designed so that you could stumble upon the garage and skip right to project purity without having to actually track down James.