Hey, new player, myself! I was looking through the forums to find info on finding Red Clay easier as I'm having issues, and ran across this.
Trying to find Red Clay for the first time is apparently hard enough as it is - I and a friend spent hours looking, and I still haven't found any. But the idea of a new player logging in for the first time and then fruitlessly looking for red clay because they got unlucky and unknowingly spawned in the "wrong" biome is a genuine problem. I would even go so far as call it a minor design flaw since it can leave a sour taste in new players' mouths, as OP demonstrated; since clay is so essential early on and most everything you want to do is locked behind it, that can lead to player frustration as they scour the land looking for what they need to "start the game proper".
My recommendation, if possible, is to add a basic toggled-on world-gen option that allows a player to guarantee they spawn in a biome that can generate red clay; that way, it'll hopefully just be a matter of time for them to run across it naturally.
If you want to go the extra mile for new players, maybe even make it so it will guarantee a red clay deposit generates on startup in a *relatively* close radius to initial spawn, too? Heck, you could even look into an advanced option where the player can choose what biome type they spawn in, so veterans can give themselves a break or a REAL challenge!
Failing that, a "simple" fix would have the game print out what biome the character spawns into, and then state whether it feels that the basics (starting food, wood, clay, etc) can be found nearby or not. At the very least, this will give new players the info they need to choose to respawn if their RNG sucks.
Thanks for your time reading this, and excited to progress when I'm able!
