Did you happen to go to the FAQs page and scroll all the way down to the Payment Status section?
https://www.irs.gov/coronavirus/get-my-payment
[Scroll down to "Questions about Get My Payment" and then click on the Get My Payment FAQs link]
I got the same message you did and went to the FAQs page. When I scrolled down to the Payment Status section and clicked on the "Different Stages of Payment" subsection, for the "Payment Status Not Available" message, it says it means: "You didn’t file either a 2018 or 2019 tax return, or you recently filed and the return has not been fully processed." In my case, it sounds like my return hasn't been processed by the IRS yet.
There's also an FAQ "Why Am I Getting Payment Status Not Available" & Answer: "If you recently filed your return or provided information through Non-Filers: Enter Your Payment Info on IRS.gov. Your payment status will be updated when processing is completed."
However, there seems to be another workaround. I was also able to verify [which you should probably also try] the current status of my return for the stimulus check on the IRS "Check My Refund Status" web page which shows that the IRS received my simplified 2019 return and that it is still being processed, but hasn't been approved yet. It specifically says "We have received your tax return and it is being processed."
Go to: https://www.irs.gov/refunds
This might be an alternate work-around until the "Get My Payment" page shows updated status info. Although technically I am not getting a "refund" due to 0 income in 2019, the "Check My Refund Status" was still able to verify that it had received my return, so at least the status of the return approval can be tracked here.
NOTE: When you click on the "Check My Refund Status" link, it will take you to a page where you can enter your SS#, filing status and refund amount. If you aren't getting a refund and only filing to get the stimulus check, then you can enter $1 for the refund amount. I found that 0 does not work, however when I entered 1 (according to a message in the system which said to do this if the refund amount is $1 or less), it then allowed me to see the current status of my "refund" as "return received". There are 3 status stages: "Return Received", "Refund Approved" "Refund Sent".
There was also another message under the "Return Received" area: "If you filed a complete and accurate tax return, your refund should be issued within 21 days of the received date. However, processing may take longer under certain circumstances."
This IRS message doesn't specify anything about TurboTax in particular, so we can't tell whether there has been a delay for non-filers in processing the stimulus checks or not due to TurboTax or due to the IRS. If you are able to verify that your return has been received via the "Check My Refund Status" page, then I would consider that to be the correct official IRS status, and just keep checking that in addition to the "Get My Payment" page until you get more updated info confirming when a stimulus check will be sent.
I have filed with TurboTax every year for over a decade and usually always received my direct deposit refund in under 2 weeks. So hopefully nonfilers who used the nonfiler TurboTax electronic form will be able to get their stimulus checks starting next week (or at least a status of it having been approved and a date for when it will be sent).
So it looks to me that it is best to check both the "Get My Payment" web page and the "Check My Refund Status" web page to verify the status.
