The custom PC is, and should be, a blank slate. The story of that character isn't mired in who they were, but in who they are going to become over the course of the game's story, so our "custom" story is the game's narrative.
I feel like I just want to jump in here with a small aside related to character development and feeling of attachment and investment.
Our character does not need to be, and ideally, in the best case situation, should not be, a blank slate... they should be someone we can define the history of, to a reasonable extent, and play them forward from there with that investment taking root backwards as well as moving forwards with them.
I want to make a special mention of Varnhold's Lot, a side story that came as DLC for Pathfinder: Kingmaker. In this side story, you play a new character, not the character that your main game file is based on, in events that take place analogously to the main game - the two characters can even eventually meet, possibly. Now, you don't get very *long* with this character; the side story is only about equivalent to one chapter of the main game in size... but the story does some truly wonderful work to create a feeling of depth and history and involvement that you, the player, take a strong role in crafting and being responsible for.
At first, I was perturbed to have to make a new character that I knew nothing about, but who was apparently part of this group of other NPCs that she had history with... and yet by the end of that single chapter story, I felt deeply attached to the character, responsible both for her, and for her bonds and relationships with the rest of the crew. I felt their history, and it felt real... and it felt that way because I helped it to grow, even if what was growing was growing backwards into their past; I directed it and defined it, and so even though I'd only been playing the character for the space of a few days to a couple of weeks in in-universe time, the romance and relationship that occurred there managed not only to NOT feel rushed or forced, but to feel satisfying, close, personal, intimate and like it had been a long time coming. It was beautifully done, and it doesn't get enough credit.
It did all of this with simple dialogue and conversation, in a way that felt natural and flowed well... and moving forward, a lot of it genuinely had an impact; the game remembered how you'd set things up, and may of your future dialogue options were shaped by the details you'd defined about your past. There are many other ways I could have defined that story and history, too, with vastly different outcomes.
Other games do this to a lesser extent (NWN2, for example, gives you some options to define a few elements of your history during the harvest festival introduction as you talk to other characters), but none I've played has ever managed to evoke such a potent feeling of connection, over such a short space of time, than this one.
The origin system is deeply flawed and is actually inherently destructive towards the concept personal character investment, in many ways that have been discussed multiple times over by others, and I don't have the energy to get into that again, but I did want to speak to this other aspect of the conversation; There is no excuse, in today's game market, for our personal character to be a bland, blank empty nothing that serves no function to the story, cannot possibly be the leader of this group of superstars and strong-willed individuals, and whose existence is so categorically valueless to the game (even the other party members banter on the road... with each other, and never us, ever. We're never involved.), like it is now. No excuse whatsoever.