Enough money to survive on ramen for a few months and build a demo. Get feedback from users and iterate over and over.
Not every company that goes through YC are at the same stage. I've heard of companies joining YC despite already having over a million in ARR because of how valuable the YC network is.
YC invests 125k in each team, which is certainly enough to last more than a few months eating ramen if you are building the product yourself.
Also, trying to sell a product using a demo is not exactly the same as selling a finished product. At 0-1 stage, you can bet the demo hides the rough edges to some degree.
I would say selling using a demo falls somewhere on the sell-before-build spectrum, but one point I was trying to make is that it is not necessarily black-and-white.
I can guarantee you won't find anything Paul Graham has written about doing a bunch of marketing analysis as a first step.
No YC company is literally in stage 1 of its existence. First you need to get into YC, and you probably won't if you don't know anything about the market you are trying to reach.
This is indeed the original idea behind YCombinator. That was a very long time ago. Things have changed, both with the YCombinator company and the ethos of this web community.