Final answer:
The Louisiana Purchase in 1803 was the initial event that led many settlers to move west in the 1800s, as it opened up new territory for exploration and settlement.
Step-by-step explanation:
The event that first led many more settlers to move west in the 1800s was the Louisiana Purchase. In 1803, Thomas Jefferson arranged for the purchase of land from France, which doubled the size of the United States and provided new territory for exploration and settlement.
The Louisiana Purchase prompted Jefferson to send Lewis and Clark on their famous expedition, paving the way for future settlers and igniting the American pioneer spirit. Although events like the Gold Rush and the establishment of trails such as the Oregon Trail were significant in promoting westward migration, they followed the initial push given by the Louisiana Purchase.