I think it's the first killing quest that gives you a block of clay as a reward.
The first killing mission is "First Blood", and it doesn't give any clay as a reward.
I've done just about everything I can up to the point of needing the clay. I've done the "Taint Nuttin" quest about 3 or 4 times, but the problem is none of my gardens are spreading across plain dirt, even after days of waiting, so that's very very slow without a watering can. I am approaching the point of having enough aluminum to make a metal bucket, but that doesn't help me past the "Fluid Favour" quest requiring you to make a clay bucket. Honestly, I feel like the "Barrel of fun" quest should reward you some clay, because without it I'm crawling along, and not really enjoying the journey.
Edit: there's quite alot of things that NEED clay to progress, like the bucket, juicer, and blank patterns. I'm pretty much at a standstill without some decent quantities of it.
Also, just noticed, hunger overhaul (annoying mod) is set to 50! yet you provide the same food over and over (trail mix) in quest rewards. 50 is a bit extreme. I realize you want a challenge, but early game this feels over the top, especially since you lose hunger simply by walking.