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.
To check on regular tax refund status via automated phone, call 800-829-1954. (This line has no information on Economic Impact Payments.)
https://turbotax.intuit.com/tax-tools/efile-status-lookup/
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. Many refunds are taking longer during the pandemic.
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 20 of your 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://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions
https://ttlc.intuit.com/questions/2840013-does-accepted-mean-my-refund-is-approved
To call the IRS:IRS: 800-829-1040 hours 7 AM - 7 PM local time Mon-Fri
Listen to each menu before making the selection.
First choose your language. Press 1 for English.
Then do NOT choose the first choice re: "Refund", or it will send you to an automated phone line.
Instead, press 2 for "personal income tax".
Then press 1 for "form, tax history, or payment".
Then press 3 "for all other questions."
Then press 2 "for all other questions." It should then transfer you to an agent.