Depending on your wife's starting corral, her actual race start time may be anywhere from 5:0 to 6:30, and depending on her race pace, she could end up at TTC anywhere from 6-7:30 or so.
Relying on Disney transportation, your main option is to take a race bus to Epcot and then monorail to TTC. Buses usually run between 3-5 am, with runners suggested to be on board by 4. Buses stop running between 5-7 and start again at 7. With this in mind, get on a bus between 4-5. If you get to TTC very early, you could always walk to Poly and get a coffee.
The only other alternative would be to take a cab directly to TTC. Road restrictions will be in place, so allow extra time to get there--and have the driver take a left out of Pop, up to Osceola Parkway, take a right on Osceola up to World Drive and right onto Wolrd Drive to MK/TTC.