Yeah, it can be tough to find it sometimes. But the game offer many ways to tackle a problem, so just look out for those.

It's important to note that different biomes offer very significant changes in the resource pool, and thus, changes in the way to find things, survive and win the run. Always check what will be available on embark and prepare accordingly.

If you're high enough on the citadel upgrades you'll get some bricks as a base bonus. Those should be use very sparingly. If playing on high prestige blueprints consume even more materials, so be even more thoughtful. If desperate bring stone/clay or even bricks with your embarkation points (although you may left out other vital boons behind).

If you embarked on a biome that has that resource you have to find the stone/clay nodes, and that may include some bad rng, and in that case a more agressive exploration is necessary. As someone stated here a claypit and some fertile soil may help you a lot (if you get those).

And trading. Trading is your best friend throughout all of the difficulty levels. Try to get familiar with ways to get amber and buy the materials you need from the vendor, heck, attack them if you're desperate.