As a GM, I used to struggle with player backgrounds and PC complexity. I thought that every PC needed to be extensively plotted out down to the tiniest detail, and ignored the fact that many players don’t enjoy doing this.
Once I took off my blinders and looked at things from a different perspective — and once I’d seen for myself how enjoyable PCs who start off simple could be — this hangup fell by the wayside.
Because just as pressuring your players to write lengthy backstories  doesn’t tend to end well, forcing them to start a campaign with a complex character isn’t the right approach either.
Sometimes, the most enjoyable player characters are those who start out as light sketches — little more than a handful of ideas and a dash of personality that someone thought would be fun to explore during play — and then become more and more complex and nuanced as the game progresses.
In other words: When it comes to player characters, emerging complexity is a fine approach.
The next time one of your players shows up for the first session of a new campaign with a simple PC concept and little to no backstory, make sure that they did so by choice (and not out of frustration, or because of writer’s block), and then just roll with it.
If there are specific things you need to know, ask for them (just don’t ask for too much at this stage) — but apart from that, let sketched-out characters like this evolve during play. Offering to help your players hone their PCs before the game  is always a good idea; just don’t be offended if they don’t need help.
You’ll find that quite often these characters end up being more interesting — and even more complex — than those who started off fully developed, complete with massive backstories. It’s easy to paint yourself into a corner with an over-developed starting PC; one of the nice things about starting with less is that it leaves lots of room for more.