One doesn't have terribly much to do with the other. Smallpox was introduced to the Americas in 1520. The only recorded attempt to deliberately infect Native Americans with it was in 1763 by a British officer. By 1803 the US government was already running smallpox vaccination programs for the Native American tribes with which they had contact. Not that the later Manifest Destiny actions weren't horrific and devastating, but they had nothing to do with creating an idea of a clean continent using disease. 19th century Americans were more than happy to invade and seize land that was fully inhabited.