Can the federal taxes be returned before the state ones if I filed them the same day?

[VolvoGirl]

Yes.  Federal and state come separately from different places at different times.

IRS Where's my refund https://www.irs.gov/refunds/
Make sure you are using the refund amount from your actual federal tax return and not the combined amount Turbo Tax showed you at the end.  That was for federal and state combined.

Check for a state refund     https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund