No, NASA did not exist at the time when the planet Neptune was discovered. The discovery of Neptune is credited to a collaborative effort involving several astronomers and mathematicians. In the mid-19th century, the French mathematician Urbain Le Verrier and the British astronomer John Couch Adams independently predicted the existence and approximate location of a yet-to-be-discovered planet based on anomalies in the orbit of Uranus.
Le Verrier sent his calculations and predictions to Johann Gottfried Galle, an astronomer at the Berlin Observatory, on September 23, 1846. Galle received the message and, on the same night, using the coordinates provided by Le Verrier, successfully observed and identified the planet Neptune. This marked the official discovery of Neptune.
The announcement of Neptune's discovery was made jointly by Le Verrier and Galle, and it quickly garnered international attention. News about the discovery spread through scientific circles, astronomical societies, and the general public in the following days and weeks.
NASA, the National Aeronautics and Space Administration, was established on July 29, 1958, more than a century after the discovery of Neptune. While NASA has played a significant role in space exploration and discovery since its inception, it was not involved in the initial announcement or discovery of Neptune.