I'm not sure - I'm sure it is possible. I do know that basements are not common in central Texas.
Near the hills there's a ton of limestone, and farther east I think there's a lot of clay. Both make digging (or sealing) a basement more expensive then in other parts of the country.
Without knowing anything about how the cost compares, it might make sense to look into building a home out of some thick dense walls of cement or something for natural insulation.
And you can look into some of the passive temperature regulation of traditional architectures from parts of the world with similar climates or newer green architectures that accomplish similar.
There are probably architecture firms in Central Texas that could help you with the last one.
I have found someone in Colorado who specializes in underground/earth sheltered homes. But local Texan expertise is even better as they’d know what has and hasn’t worked for local conditions.
Near the hills there's a ton of limestone, and farther east I think there's a lot of clay. Both make digging (or sealing) a basement more expensive then in other parts of the country.