TurboTax gives you an estimated date for receiving your refund based on a 21 day average from your date of acceptance, but it can take longer. “21 days” is not a promise from TurboTax or the IRS.
First, check your e-file status to see if your return was accepted:
https://turbotax.intuit.com/tax-tools/efile-status-lookup/
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 35a of your 2023 Form 1040) of your federal refund to track your Federal refund:
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://ttlc.intuit.com/questions/2580357-who-provides-the-refund-processing-service
https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions
You said you didn't get any emails from Turbo Tax? When did you efile 2023? Was it Accepted? Did you go all the way through the File tab, through the 3 steps and hit the big orange Transmit Returns Now button? Maybe you didn’t finish filing it or it rejected or you were suppose to print and mail it.
Check back though your emails. When you efile you get back 2 emails. The first email only confirms the transmission. The second email says if the IRS (or state) Accepted or Rejected your efile. If you efiled there should be an Electronic Postmark page. Probably near the end. That is your proof and signature
When you log into your account you should also see the status and if it was Accepted or Rejected, Started, Printed, Ready to Mail, etc. What does it say?