SPOILERS* Technically, she never could've made it because this version of Elizabeth, who really loved Paris, stopped existing in all possible universes once Booker was drowned. The only universe(s) where Anna now exists is (are) the ones where she grows up with Booker and Comstock never kidnapped her.
Thanks! Not to get into a huge multiverse debate, but I think it's flawed to think that there's only one universe similar to the events of infinite. Fun stuff though, that's the cool part about the game. Everyone has their own theories