Geography was a big part.

The Spanish, French, British, and Portuguese were at an advantage from the beginning geographically, since they sort of jut out into the Atlantic. That's why these empires flourished while the Swedes failed and the Dutch had very little by comparison. The failed empires were further from the action, and since these big powers, that they would often have rivalries with, were in between them and the New World, getting past them could not have been an easy task. And the Dutch probably had a hand from their friendship with the English after the Glorious Revolution.

Now, given that information, how well would the Ottomans have fared, seeing as trying to send any ships through the Strait of Gibraltar, the only possible route, for the purpose of taking these highly-contested lands that would no doubt have caused friction with the Spaniards? And considering Spain was the most powerful naval nation on earth due to its empire for quite a while, an Ottoman attempt to fight their way through the strait would likely fail.

Now, as for China and Japan. These ones aren't as obvious, since they seem to have a clear shot to the Americas, and China was home to the great mariner, explorer, and diplomat Zheng He. So why didn't they just head east?

The reason for Japan likely has to do with it's internal politics, from the mid 15 to early 17 centuries, Japan was in what is called the Sengoku period. Put simply, the Sengoku was a massive, multi-sided, ongoing civil war between assorted Daimyō clans. This disunity likely would have prevented any efforts from the Imperial government to explore or expand eastward. And once this chaos finally ended in 1603, the new government, the Tokugawa Clan, was isolationist, and likely didn't care for anything outside the archipelago.

For China, I'm not as sure as to why. But, if you look at the Ming dynasty's history, you'll see that after Zheng He's great voyage, nothing else like it was ever done. That's because Zheng He wasn't really sent out as an explorer by the Qing, although he certainly did a lot of that. The reason the Yongle Emperor likely sent him out was to spread the word of the Ming's greatness and hopefully try to get some influence in the Indian Ocean region. If you look at some of the documents from Zheng He's voyage, particularly the one dated December 28, you'll see the emphasis placed on the people of Cochin's supposed reliance on and subservience to China. This, I think, is an indication that the voyages were used mainly as a propaganda tool for the Ming, and Zheng was their proxy. After Zheng came home, the mission to spread the Ming's glory complete, China just didn't have any interest in continuing such ventures.