Is there a way to start an IRA or a Roth IRA account using Turbo Tax before tax refund is submitted?

You can start an IRA or Roth but not via TurboTax.  TurboTax cannot start an IRA for you.    You have to use a financial institution that can start a retirement account for you.   If you want to get one opened and file by April 18, 2021 you can enter an IRA contribution on your 2021 return.  

You must also fund the IRA no later than April 18.

I should add that if you are hoping to get a deduction on your 2021 tax return, you had better learn the difference between a traditional IRA and a Roth IRA and understand the differences in what you can deduct on a tax return.

All set!  Thank you!