my tax refund

No, there is nothing you can do to speed up the IRS processes.

After the tax return has been Accepted by the IRS (meaning only that they received the return) it will be in the Processing mode until the tax refund has been Approved and then an Issue Date will be available on the IRS website.
See this IRS website for federal tax refund FAQ's - https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions

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:   

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://ttlc.intuit.com/questions/2580357-who-provides-the-refund-processing-service

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

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.

https://ttlc.intuit.com/turbotax-support/en-us/help-article/internal-revenue-service/federal-refunds-delayed-due-path-act/L5jnQJsBi_US_en_US?uid=lrrwpybr

https://turbotax.intuit.com/tax-tips/irs-tax-return/what-is-the-path-act-and-how-may-it-impact-your-taxes/L2fkZJmNC