First, check your e-file status to see if your return was accepted: 

https://turbotax.intuit.com/tax-tools/efile-status-lookup/

 If accepted, they try to process it within three weeks but it can be longer.  This year if you have earned income credit,  additional child tax credit, unemployment  and/or  the repayment of the Premium Tax Credit then your return could be delayed in processing until sometime in May.

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:   

https://www.irs.gov/refunds

Im in the exact same boat, I filed 3/16/21 and still nothing from my state or federal... My state says processing while the IRS shows no info available... Frustrating afff

Thank for your reply. My refund  for Federal and State has been accepted. 

Sadly the IRS has more than it's share of issues this year so until they get to your return in the millions that have piled up you will just need to be patient.  Check the IRS site once a week for a progress report.