TurboTax gets no information about the status of your refund.
In normal times, the IRS says that most filers get their refunds within 21 days from the time their tax return is accepted. Some refunds take longer.
Many returns are taking longer now since the IRS did not process returns for a while and there is now a big backlog of unprocessed returns. The IRS is currently not processing any mailed returns. 

If you efiled your return, have you confirmed that the return was submitted and accepted by the IRS?
https://shop.turbotax.intuit.com/efile/efile_status_lookup.jsp

If accepted, what does the IRS tracking web site say about the status of your refund?
https://www.irs.gov/refunds

Here is an IRS Q&A with information about refunds:
https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions

The IRS can look at your 2018 or 2019 return to issue a stimulus check.  If they do not have a 2018 return then you may be waiting for them to finish processing 2019 before they will be able to use it to issue your stimulus check.

If you used the non-filer site, you will not be able to e-file a 2019 return after using the non-filer site.

TurboTax has no control over your stimulus check, nor can TT track it for you or tell you when the IRS will issue it. Refer to the sites linked below:

You can call the IRS hotline at 1-800-919-9835 to get updates on your stimulus payment.  

https://www.irs.gov/coronavirus/economic-impact-payment-information-center#nonfilertool

https://www.irs.gov/coronavirus/get-my-payment-frequently-asked-questions

https://ttlc.intuit.com/community/tax-topics/help/how-will-the-stimulus-package-impact-me/00/1393859