The title pops up in the very first chapter, when an awestruck Bobby is holding his daughter. Check it out:
But I figure if the world were really right, humans would live life backward and do the first part last. They'd be all knowing in the beginning and innocent in the end.
Then everybody could end their life on their momma or daddy's stomach in a warm room, waiting for the soft morning light. (1.12-13)
What Bobby is saying here is that humans start out innocent and end up with knowledge… but that this should work in reverse: We should come into the world with knowledge, and dwindle into innocence as we approach death.
So here's what's up with title: It's a shout-out to this passage above, yes, but more than that, it's a shout-out to how much Bobby feels like he's in over his head in this book. Feather might technically know less than he does, but Bobby feels clueless when it comes to parenting—he wishes he could start with the know-how he needs instead of having to wait for it to accumulate through experience.
More generally, the title—The First Part Last—references the topsy-turvy nature of Bobby's life. Just like time is messed around with in the title, Bobby's plans for his life are majorly messed with, too, when he becomes a parent. The title gives readers a heads-up, then, that things in this book just might not go according to plan. And they don't, in so many ways.