What should I do if I received a 1095-A form where all the amounts in the boxes under Coverage Information are zero but TurboTax is telling me that's not possible?

Look to see if it is marked VOIDED. If so, ignore it. If you actually have coverage from the Marketplace, there should be real numbers. Contact the issuer. You will need a corrected 1095-A.

From the IRS:

About Form 1095-A, Health Insurance Marketplace Statement

Publication 5223, General Rules and Specifications for Affordable Care Act Substitute Forms 1095-A, 1094-B, 1095-B, 1094-C, and 1095-C

Corrected, Incorrect or Voided Forms 1095-A