How do I know if my return was approved?

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.  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:   

https://www.irs.gov/refunds

To track your state refund:    

https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund

https://ttlc.intuit.com/questions/1901548-why-do-some-refunds-take-longer-than-others

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.

https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions

https://ttlc.intuit.com/questions/2840013-does-accepted-mean-my-refund-is-approved

https://ttlc.intuit.com/questions/2724106-my-return-is-accepted-but-still-not-approved-is-there-a-problem-should-i-be-worried

https://ttlc.intuit.com/questions/3397970-path-act-delayed-refunds-for-some-filers