Did you use the IRS non-filer site? If so, that is all you have to do.
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.
You can also simply sign back in under non-filers portal, since you have already used it, click on the ' Check E-file Status' by typing your social security number there, it will show you your current status from the IRS.