No, the issue in 1492 was not whether or not the Earth was a sphere. What was at issue was the size of the Earth, & whether a westward ocean route could be found to the Far East. Europe had traded with the Far East via a long overland route running through central Asia, for almost a millennium. This route was long, & dangerous & expensive to travel. But the Europeans prized many things which came from the Far East, such as silks, & certain spices. If the world was a sphere, many reasoned, then traveling west would take you to the Far East.
What was unknown, at this time, was how long such a route would be, or if it was navigable. A number of mariners & scholars had dabbled in measurements of the Earth, but came up with conflicting numbers for how big it was (& therefore how long a westward route to the Far East would be).
His speculation was that the Earth was about 1/4 as big in diameter as it actually is. Thus, he was convinced that the Far East was only a few thousand miles west of Lisbon. His conjecture, therefore, suggested that a westward sea route to the Far East could be quite profitable. It's possible that he allowed himself to be convinced of this by Icelanders, whose tradition had told of a great land not far to their west, "Vinland," to which one of their heroes of old (Leif Erikson) had gone. He may have surmised that these Viking explorers had arrived in the north of the Far East.
He tried to get the Prince of Portugal to finance an expedition, but was rebuffed. He turned, therefore, to the king & queen of Spain, Ferdinand & Isabella. He made a series of presentations to them, & they appear to have vacillated for a time, before deciding to finance a voyage.
Columbus believed he had arrived in India. For this reason, native Americans were mislabeled "Indians," a mislabel which has since stuck & is still used today. He was convinced of this, not only due to his speculation about the size of the Earth (which he'd underestimated enormously), but the "Indians" he found bore some resemblance to what he'd heard about the people of the Far East. In this regard he was actually somewhat correct; as it turns out, native Americans, & the majority of people of the Far East, are of Mongoloid descent.
Columbus left some men behind on Hispaniola, & returned to Spain, to great acclaim. It was only later that it was determined that he had not actually come to the Far East, but had landed at an intermediate point.
Furthermore, his effort to find a westward oceanic route to the Far East was undermined, when the Portuguese explorer Vasco de Gama found a way to reach India, via an eastward route, beginning southward around the southern end of Africa. Later, another Portuguese explorer, Ferdinand Magellan, would lead an expedition that did, actually, circumnavigate the Earth (Magellan himself died near the end of this voyage). Magellan's voyage showed that de Gama's route to India was shorter & therefore preferable to a westward route.
The English also sent expeditions to compete with the Spaniards'. The most notorious of those who competed with them was Francis Drake, the second explorer to circumnavigate the Earth.
This New World opened up new opportunities. It had resources which, until then, had never been dreamed of. It also had a wealth of new things, to which Europeans took immediately. Corn, tomatoes, potatoes, & tobacco were all discovered in the New World; they later became staples in Europe. Furthermore, the Americas had gold reserves which had, more or less, gone untapped by the native Americans.
Discovery of the New World created new opportunities for wealth, for those in a position to exploit it. The trading companies of England, for example, had languished in obscurity, until navigation to India & the New World was opened up. It would lead to the rise of the middle class in Europe, which in turn fundamentally altered European society. The New World also promised hope for those who had none, at home; for example, the Puritans came to the New World looking for freedom from persecution.
The opening of the New World was part of a larger change, the dawn of the Age of Enlightenment. The two went hand-in-hand, & the world would never be the same again.
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