The TurboTax online editions for tax year 2020 should be available in early December.

The TurboTax desktop CD/Download editions for tax year 2020 should be available by mid-November - https://turbotax.intuit.com/personal-taxes/cd-download/

Although the beta versions of the program come out early they are not fully functional until sometime late January at best and many forms including the state programs are not complete until late Feb or sometime in March.  The IRS efile start date is still TBD however in the last couple of years they have not opened until very late in January.