Gonna say you’re way off there. Once you decompress common crawl and index it for FTS and put it on fast storage you’re in for some serious pain, and that’s before you even put it in your ML pipeline.
Even refined web runs about 2TB once loaded into Postgres with TS vector columns, and that’s a substantially smaller dataset than common crawl.
It’s not just a dumping a to of zip files on your NAS, it’s making the data responsive and usable.