No one can answer that for you. Only you would know what date you put your tax return into an envelope and took it to a mailbox, unless you used a mailing service like certified mail that gave you a dated receipt. TurboTax has no way to know when you mailed a tax return.
When you mail a tax return, you can expect it to take considerably longer to process than an emailed return, so all you can do is wait until a human opens your envelope, enters the information into the system and then you can watch for information about your refund on the IRS refund site. TurboTax will not get any information about your refund.
You need your filing status, your Social Security number and the exact amount (line 35a of your 2022 Form 1040) of your federal refund to track your Federal refund:
P.S. I hope you do not believe that TurboTax mailed your return to the IRS for you. TT does not mail it. You have to print, sign and mail it yourself if you chose to file by mail.
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