Unfortunately, you're at the mercy of the Marketplace.
Often taxpayers can view the form online, but that assumes they've
already prepared it and sent a copy to IRS.
If you file without the 1095-A, and you received a subsidy
(Advance Premium Tax Credit) to help pay your health insurance premiums, the
chances are strong that you'll wind up receiving a letter from IRS asking for
the form 8962 & the 1095-A anyway. And that will mean additional time
& effort on your part, not to mention the potential for a refund hold.
If you're certain you received no subsidies, then filing without
the form could possibly affect your return by not including an amount of
Premium Tax Credit which you may be eligible for. So it cuts both ways.
Best to wait until you have the form before filing.
We're still a month from the filing deadline, so give it
time. I would call them back if you haven't received it a week before the deadline. If they tell you it won't arrive until after the deadline, then you should file an extension (Form 4868, which you can do in TurboTax). This is probably not something
you'll want to do, but you have little recourse without the 1095-A.
