I don't make Sims very often, but when I do, it really depends.
Sometimes I have a really clear idea in mind of what I want a Sim to like and what their story will (although, that last bit can change as I play). For example Sadie, who turned out exactly as I wanted her:


At other times I just randomise until I get something I can work with, tweak it a bit or a lot, give them some better clothes.
Sometimes I go for traits first, when I sort of have a type of Sim in mind, give them the traits and aspiration and then randomise until I get a Sim that suits them.
I'm also really fond of the genetics generator - I just made brothers and cousins for Stephanie and also a sister and a brother for Adam :)
Stephanie's brothers:

I also like coming up with backstories, but that's just to make them sound more interesting, I don't always play them according to their backstory.
I just realised none of this really answers your question, does it? Sometimes, characters have existed in my mind for ages, like Stephanie and Adam or, more recently, Finn:

Aside from that, I usually just randomise and sometimes there's a Sim I like that, the moment I see them, immediately gets a background, plans for the future, etc. Like Jing-Mei:

Comes from a traditional Chinese family, recently moved to Newcrest, now lives with a roommate called Molly. She's creative, loves to cook, but none of your typical take-away food, haute cuisine is more her style - although she still needs to learn a lot about cooking.
I can go on and write up an entire story, for me, once I get started the ideas often keep flowing.
My advice to battle your CAS block: randomise (and don't be ashamed to click that button 60 times or more - I have done that, I'm very picky I guess).