We've received a purchase order for $200k of corrugated packaging
materials from a company based in Bejing with terms FOB our United
States location. How do we secure payment up front -- before we begin
manufacturing?

You need a commerical letter of credit.  This site explains:
http://www.crfonline.org/orc/cro/cro-9-1.html

Since you want to delay manufacturing until you have assurance of
payment, the shipping/expiry date should be appropriate to allow for
your production time.

IF you have any questions, please let us know.