I fully understand that people starting out in consulting work don't want to do this, or can't. That's OK. But I don't think it's a good idea to build this constraint into your practice as a principle; it will keep you from growing your business.
The way Jeremy and I started Matasano --- it's probably more accurate to say the way Jeremy started it, since he's ultimately the person who founded Matasano, back when it had its original name, for his cat --- was to do "serious" consulting projects on the side while working a full-time job. I don't think he was taking prepayment for those projects, and if he was, I sure didn't see any of that money. So that's one way to maybe start consulting without depending existentially on up-front payment.
I also understand that there is a class of client --- one I think people new to consulting believe is much easier to acquire --- that can't reasonably be trusted without prepayment. I agree that's a thing, too. If you need these clients to boot up, that's fine, and I'm not dragging people for taking them. But here's a constraint you should build into your practice: your mid-term goal should be to say no to these clients, full stop, not trying to find a way to fit them into your pipeline.
Also: I can only tell you what's worked out for me and the weird group of people I know. I feel pretty confident about this stuff as business advice but I could obviously be wrong. I'm not going to waste everyone's time tediously disclaiming that though (this one tedious disclaimer excepted).