1) Train an initial big model on everything you can get, yielding a capable but tainted-in-some-jurisdictions model. Keep that model private.
2) Use the big tainted model to narrow or distill the source data. One way is by identifying the document subset that can be used freely (old public domain works, user generated content uploaded to your own service that users already assented to your own company's ToS on, government documents, things with unrestricted Creative Commons licensing...) The other way is by using it to build "just the facts" distillations from restrictively licensed material.
3) Train an untainted model using just the factual distillations and/or the permissively licensed material.