How could the people in Battlestar Galactica end up on Earth when they were there at the start of season 4.5 and it was nuked?

The answer requires a little background. First, there were really two "Earths". The first Earth was mentioned in the mythology of the 12 Colonies. While the 12 colonies left the planet Kobol to settle the 12 planets (Caprica, Geminon, etc.), "Earth" was the destination of the 13th "Lost" colony. It was this "Earth" that the people of Battlestar Galactica found, but unfortunately, the inhabitants of this Earth had a catastrophic nuclear war that completely devastated the planet.

Fortunately, the location of a different Earth was known by a Starbuck's father. While several good explanations as to why he knew this information have been put forward, regardless he taught the FTL coordinates to Starbuck in the form of a melody. In the final episode, when instructed by Adama to enter coordinates for a "blind" FTL jump, Starbuck entered the mathematical equivalent of the notes of the melody. The resulting jump put them close to a planet already inhabited with primitive humans (as it turns out, our own primitive ancestors). Adama names this unknown planet Earth.