Global Store Ships from Multiple Countries - What to Enter for Country of Origin?

Hi, I sell print-on-demand products. My print-on-demand provider ships from many different countries, so a product gets produced at the factory closest to the customer, for faster shipping. I use Matrixify to update product details in bulk, and one of the columns in the product csv is “Variant Country of Origin” and “Variant province of Origin.” Can I just leave these blank?

Any help understanding this would be greatly appreciated:)

Thank you!

Amanda