I've been searching everywhere but I can't find any information on what the starting funds for a level 1 warrior is. Do they not get any?
Actually, NPCs get significantly more than (most) PCs at level 1! You can find the relevant funds here-- it's unfortunate that they aren't listed in the class descriptions like the PC classes nor the WBL section, but that's probably because all NPCs get the same funds and also they have to spend them a little differently.
A typical first level Warrior has 50 gp worth of weapons, 130 gp worth of armor and other protective equipment, no permanent magical stuff not included in the previous two categories, 40 gp of consumables like potions and scrolls, and 40 gp of other miscellaneous non-magical gear.