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:
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