Why was Thermopylae the first step in the creation of more unified Greek nation?

It did not - there was never a unified Greek nation until over 2,000 years later.

After the Persian invasions were repulsed, the Greek city-states went back to fighting each other with reneewed vigour. This culminated in the Peloponnesian War which, over 27 years, devastated the Greek world. Even after this disaster, the in-fighting persisted, and after a brief period of control by Alexander the great, it split up into various kingdoms which continued to fight each other, until they were brought within the Roman Empire which quietened them down by strict governance.