In the Caribbean and the mainland of the Americas during the 16th century, Europeans were seen in a variety of ways. When Columbus first landed in the New World, he encountered groups that struggled to understand European interests and culture. Caribbean society was constructed through a unique trading system governed by elites who maintained power by marrying within elite spheres. Columbus and his men were interested in odd things compared to local trading requirements: Columbus wanted gold, pearls, domesticated animals like monkeys, and jewelry. Taino Caribbean peoples were used to trading gold to be used for elite jewelry, but more effort was put into acquiring cotton mantles, weapons, stone and copper tools, and manioc flour. In exchange for goods that were not the backbone of the Caribbean trade network, indigenous groups could acquire clothing, glass beads, and shiny baubles. Why are these useful? They are decorative and local elites might be willing to offer quite a bit for them. That might explain why on Christmas Day of 1492 Columbus claimed that more than a thousand indigenous people crowded his small fleet to try and trade for goods. As European demands for goods increased and awful stories of European actions against nations within the Caribbean structure spread, Caribbean peoples began to use force to signal the end to their basic trade relationship. Were they significant? Not to the political elite, at first. As Columbus and more Europeans returned to the Americas bringing more men and trade goods, however, that changed. Europeans shifted their own actions from one of curious new trading partner to clear invader. Columbus's subsequent voyages stressed colonial development, not trading posts. Hulme's Colonial Encounters: Europe and the Native Caribbean discusses this quite well. The power and freedom of the Caribbean elites was challenged as Europeans began to use indigenous labor to construct the forts, towns, and churches that would serve the Europeans in their new enterprises of gold mining, farming, and indigenous slave trading. This is just the early Caribbean. Other first contact meetings are just as varied.

For example, when Cortes arrived in Vera Cruz and began to move west, his actions were under close scrutiny. The Mexica leader, Montezuma II, had advance knowledge of European activity in the Yucatan. (The Nahua peoples may have known about the Europeans as early as one of the later Columbus voyages when the Admiral captured a trade canoe that may have been moving between the Yucatan and Cuba.) Montezuma II had several thousand men available for combat, but the Europeans were less than a thousand. Why bother with them? Other groups had similar views, some attacking Cortes directly. It became apparent to some ethnic leaders, however, that Cortes and his men were different. Their arms and tactics were different. Groups opposed to Mexica hegemonic power supported Cortes and his men as they approached the Mexica capital, but Montezuma II did not appear to see them as a significant threat. (One fun explanation presented by Restall at a AHA conference a few years ago was that Montezuma II allowed the Europeans into the city so that he could establish a special section for them in his zoo on the palace grounds.) Still, the Europeans are the other. They do not behave the way groups expected them to. Lockhart coined this relationship as "double mistaken identity" where two groups expect the other to behave using their own cultural norms. They were insignificant until it became clear that their actions were subverting local and imperial control. By the time ethnic lords saw how dangerous and significant Europeans were, it was almost too late.

Peru was no different. Why should Atahualpa mobilize his veteran army against fewer than two hundred Europeans at Cajamarca in the 1530s? True, Pizarro had the support of some indigenous groups he had met along the way, but those people were not a significant threat to Inca power. Only when the shock of horses and gunpowder upset the ranks of Atahualpa's army did the captured Inca see how he had misjudged the Europeans. (I would argue he continued to misjudge them when he carried out royal business, including the order to assassinate his brother and political rival, Huascar.)

So are they just another visitor? Absolutely. True first contact meetings between Europeans and indigenous Americas are not usually violent. Trade is attempted and is usually successful. Only when stories of European actions in enslaving populations, taking women and children, and using forced labor to acquire gold and pearls (decorative goods) do groups challenge Europeans and resist the arrival of new groups. There are some European versions of contact that often portray the Europeans as saviors or powerful beings due to their weapons, horses, and ships. Most of these interpretations are meant to be read by the people funding these expeditions so making things seem more glamorous and the Europeans more revered are expected. So, to answer your question: I would argue that the majority of indigenous groups first encountering Europeans did not see them as significant, but as a novelty and weak trading partner. There are three excellent works to read if you want to get more explanations: Whitehead's Wolves from the Sea, Weber's The Spanish Frontier in North America, and Sauer's classic The Early Spanish Main.