Federal and state refunds come from completely separate entities, There is no rule as to which one will come first or how much time there will be between their arrivals.
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 2022 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
It's all over the place...no way to predict. Some states will tend to be faster than others....but even that will vary from year-to-year
Your state and federal refund comes from two separate entities so either one could come first. You can check out this Help Article for instructions on how to track your state refund.
If the IRS has accepted your e-filed return, you can check the status of your refund by going directly to: https://www.irs.gov/refunds