This forum is here 24/7 (no guarantee that anyone can answer your question).
Phone support hours depend on the tax season. Currently 5AM - 9PM PT.
Here is a TurboTax FAQ for contacting customer support.
The user forum is available 24/7 although there are fewer of us to reply during the night. As for TT customer support or "Live" help---that is available from 5 a.m. to 9 p.m. daily, Pacific time.
Phone support is not provided with the Free Edition. If you are using a paid version of the software or if you purchased PLUS you can get phone support when customer support is there. Otherwise, post your question here and someone will try to help.
To call TurboTax customer support
They are available from 5 a.m. to 9 p.m. Pacific time