An Accidental Alliance — Jonathan Edward Feinstein

The first book in a new science fiction series. With a killer asteroid headed toward Earth and the nations of the world on the brink of a nuclear war, several thousand volunteers are selected for the audacious Project Van Winkle to provide the seed for a new civilization should the worst happen. Unfortunately, someone forgot to set the alarm and they wake up two hundred and fifty million years later, still on Earth, but in a world entirely alien to anything they knew.