How do I file my early 403(b) withdrawal with the Covid-19 exception?

You will report this on a Form 8915-E.  The IRS has not yet finalized the Form 8915-E for retirement plan distributions under the CARES act.  So this form cannot be included in the TurboTax program.  You will not be able to proceed until the form is available.

The IRS has not communicated when the form will be finalized for inclusion on the 2020 federal tax return.

We estimate it will be sometime in February 2021 before the form is available.  You can watch this link for the form availability.  Currently, the form is not listed here since there is no estimated date.  Once there is, you will find the form listed with the date available.  

IRS forms availability table for TurboTax individual (personal) tax products

Additionally, the IRS will not start processing returns until February 12, so waiting for this form is not slowing down the processing of your return.