A basic Google search for "synthetic data llm training" will give you lots of hits describing how the process goes these days.

Take this as "defeatist" if you wish, as I said it doesn't really matter. In the early days of LLMs when ChatGPT first came out the strategy for training these things was to just dump as much raw data onto them as possible and hope quantity allowed the LLM to figure something out from it, but since then it's been learned that quality is better than quantity and so training data is far more carefully curated these days. Not because there's "poison" in it, just because it results in better LLMs. Filtering out poison will happen as a side effect.

It's like trying to contaminate a city's water supply by peeing in the river upstream of the water treatment plant drawing from it. The water treatment plant is already dealing with all sorts of contaminants anyway.