There are no fixed dates or timeframes for tax refunds and stimulus payments. The IRS is working with reduced staff because of the Covid-19 pandemic. Most IRS offices are only partly open, and many employees are working from home. Everything is taking longer than normal, and there are many delays. No one can tell you when you will get your tax refund or your stimulus payment.
You might be able to check the status of your federal tax refund at the following link on the IRS web site.
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.