When will it be available that I can pay out of my TurboTax refund

Probably not until Efiling opens in January.  It's too early to efile now.  And your federal refund has to be big enough to cover the fees Plus the 39.99 Refund Processing Service charge (44.99 in California).  So you should pay upfront with a credit card to avoid the extra charge.

You cannot e-file a tax return until sometime in January.  At that time, if you are getting a refund large enough to cover the TurboTax fees, you will be able to choose to have your TurboTax fees deducted from your federal refund.  Be aware that there is an extra fee for doing that--last year it was an extra $39.99 (or $44.99 in CA).

And..... it is not a "TurboTax refund."  Your tax refund does not come from TurboTax.  A tax refund is issued by the IRS or your state.

The pay with refund option is only available if you have a federal tax refund and the refund is large enough to pay the TurboTax account fees.  The option will be available only when the tax return is completed, all the required forms and schedules for your tax return have been approved and are available sometime after January 1, 2020.

See this TurboTax support FAQ - https://ttlc.intuit.com/community/payments/help/can-i-pay-with-my-refund/01/25711