Is it normal to get state refund before federal? I filed them at the same time

Yes.  Because these two are independent of each other, it is possible to get State refund before Federal.  Unfortunately, once a tax return is submitted to the IRS it is up to them how quickly the return is process.  However, you can track the status of your e-filed return on Turbo Tax by going to Efile Status Lookup.  You can also get the status of your refund by visiting the IRS site at Where Is My Refund.  You will need your filing status, refund amount and social security number to access this site.  I would recommend that if 2-3 weeks have passed you may want to call the IRS customer service line at 1 800 829 1040 to inquire regarding the status of your return.  Also, see TurboTaxTRChrisH response below.

https://ttlc.intuit.com/questions/3753832

Yes I received my turbo state refund 5 days after accepted including weekend days.

Same here. They always seem to send out the state quicker than the federal.

It is entirely normal to get a state refund first, and then the federal. Some state forms are very straightforward and the IRS is also verifying Advanced Child Tax payments and Covid relief payments.