A bit faster since you do not have the delay of waiting for the third party bank to receive it and remove your fees and send the rest to you.
First, check your e-file status to see if your return was accepted:
If accepted, they try to process it within three weeks but it can be longer. if you have earned income credit or additional child tax credit, it will be at least the end of February before you see your refund, due to the PATH act that requires that they hold your refund longer.
Once your federal return has been accepted by the IRS, only the IRS has any control. TurboTax does not receive any updates from the IRS. Your ONLY source of information about your refund now is the IRS.
You need your filing status, your Social Security number and the exact amount (line 34of your 2020 Form 1040) of your federal refund to track your Federal refund:
To track your state refund:
If you chose to have your TurboTax fees deducted from your federal refund, that will take some extra time, while the third party bank handles the refund processing.