I know that the term "Manifest Destiny" came into vogue long after the time of America's founding fathers, but did the founders of our country like George Washington, Thomas Jefferson, John Adams, etc. believe/envision/hope that one day the United States would stretch from coast-to-coast?
Did they believe the United States would eventually takeover the other colonies situated near it or were they happy with the land they had? In essence, did they believe in "Manifest Destiny" before it was in-vogue?
There were around 55 delegates writing the constitution, and they didn't agree on many things, but they did provide for the possibility of expansion. Article IV section 3 of the constitution gives congress the ability to admit a new state. As for their views of should they expand or could they, the founding fathers were split.
However it is safe to say that most, if not all, of the men did not envision the coast-to-coast country that we have today. Jefferson is regarded as an early expansionist, but even he expected it to take a thousand years to populate the west. As you can see in this map, the territories blocking their path to the ocean were in British/Spanish possession, even after the Louisiana purchase. On top of that, the west was not that interesting. The only motivation that early America had to go that far west was to build a trade route to Asia.
The idea of "Manifest Destiny" wasn't that strong in the US until about 20 years later, and it was part of the cause of the Mexican-American war. This would be just after the Founding Fathers' time though. Monroe was the last "founding father" president in 1816 and Jefferson and Hamilton died in 1826. When the US finally touched the pacific ocean it was 1848.
The Penguin History of the United States of America by Hugh Brogan and Made in America by Bill Bryson.