After the tax return has been Accepted by the IRS or state (meaning only that they received the return) it will be in the Processing mode until the tax refund has been Approved and then a date for Sending will be available on the IRS/state website. Turbotax is not able to assist you any longer ... they are out of the loop once your return has been filed successfully.
Some states are fairly quick with refunds, while other states can take a long time processing returns--even several weeks--as they crack down on detecting fraudulent returns or face Covid staffing problems. You may be able to get an idea about how long it takes in your state from the FAQs at your state's tax agency website as I will mention below.
Of course, you first need to be sure your state return was successfully filed. Here's how:
If you efiled, be sure your efiled state return was accepted. If you used Online TurboTax, you can check by looking at the Tax Home in your Online account.
Or did you choose to file by mail instead? TurboTax does not mail it for you. If you chose that method, you have to print, sign, date, and mail it.
The FAQ below tells how to check on a state refund and has a link for your state.
TIP: While you're at your state's tax website, also look for a statement or FAQ that may say about how long it takes to get a refund in your state and how to long to wait before phoning the state tax agency. Many states have such information on their websites.
FAQ: How do I track my state refund?
https://ttlc.intuit.com/community/refund-status/help/how-do-i-track-my-state-refund/00/25571
