How did the first political parties form?

The first two political parties to emerge in the United States were the Federalists and Anti-Federalists. This division came about essentially over the ideology forging the new nation. Federalists, such as Alexander Hamilton, favored a stronger, centralized government. It was a party focused on the power of the federal government. They wanted strong relationships with Britain and supported the idea of "implied powers" in the Constitution.
The Anti-Federalists, or Jeffersonian Republicans, favored an approach more aligned with states' rights. They focused primarily on the rights of the individual and believed the Federalists to be aristocratic. You can imagine their viewpoint having substantial support because the American Revolution was still fresh in the mind of the young nation. It had just escaped the stranglehold of an aristocracy and did not need to return.
https://www.constitutionfacts.com/founders-library/first-party-system/