Federal and state refunds come from two completely separate entities, so there is no telling which one will arrive first.
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.
Once your return has been accepted by the IRS, only the IRS has any control. TurboTax does not receive any updates from the IRS.
To track your Federal refund:
To track your state refund:
https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund
On the IRS site you are also offered the use of an app called IRS2Go
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.
I would like to know which return comes 1st federal or state