Knowledge of the Pacific Ocean pre-dates the first permanent European settlements on what is now the East Coast of the United States. St. Augustine, Florida was founded on Sept. 8, 1565, while the Spanish explorer Balboa had learned the existence of the Pacific in 1512 after landing in Panama. Magellan's expedition successfully crossed the ocean less than a decade after that, and other nations followed suit, Francis Drake's famous expedition coming at the end of the 16th century.

After the 16th century, exploration of the Pacific coast of North America stagnated for nearly a century. John Speed's 1627 map of the world didn't change all that much until the first decades of the 18th century, when European explorers began to penetrate what is now the Pacific Northwest. Russians traversed the Bering Strait as early as the first half of the 17th century, but knowledge of those voyages didn't spread, and it wasn't until the 18th century that Russian voyages attracted attention to the region.

Even before the Russian exploits, however, it was thought that a strait, the Strait of Anian, separated Asia from the Americas. The strait is shown on maps as far back as the Tabula Rogeriana in 1154, even before the Americas were known to Europeans.

That said, there's an element of truth to your question. During the Manifest Destiny period of American expansion in the 19th century, it was thought that the United States of America would eventually grow to encompass all of North America, and even far-off destinations would host great populations and burgeoning cities. The growth, it was thought, would be all but inexhaustible, with even Alaska boasting populations in the millions and agriculture widespread as cold-resistant crops were developed.