No.
Once your return is filed, TurboTax has no control over the processing of your return or the release of your refund.
Here are a couple FAQs to track your refund:
When will I get my federal tax refund?
How do I track my state refund?
Why does Where's My Refund say "approved" but TurboTax still says "accepted"?
No. You simply have to wait with the other millions of people, and let the IRS process your tax return.
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 2024 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
If you are getting earned income credit on line 27 or additional child tax credit on line 28 You are subject to the delay required by the PATH act. Do not expect your refund earlier than late February.