For some things like meat, eggs, and milk: The USDA-inspected processing facility is required to be listed on the package. It is usually not very far-removed from the farm. It's coded, and these days it's usually printed near the sell-by date.

They (the USDA) publish cross-references betwixt the codes and the processing plants.

It's been kind of a pain in the ass when I've looked this stuff up in the past and I wish someone would take it upon themselves to make it easier, but it's do-able.