You may qualify for an exemption due to hardship, but you'll need to submit an application after you file your taxes to get back the penalty for not having health insurance. For situations that qualify, click here: Hardship Exemption.
During the health insurance interview, TurboTax asks Did anyone have a situation that waives the tax penalty for being uninsured? Scroll down to Had a hardship and check A hardship kept one or more of us from getting insurance. Then click the link to apply for an exemption. (Click the screenshot below for reference.)
The FAQ below provides instructions for getting to the hardship exemption section in TurboTax.
Can I get a health insurance penalty exemption? https://ttlc.intuit.com/replies/4234967