As usual, I can only speak about the Spanish historiography, but the reaction was of absolute bewilderment. The first settlers and conquistadores were completely stunned and it shows in their writings, which are many: the General and Natural History of the Indies by Gonzalo Fernández de Oviedo, Hernán Cortés' Cartas de Relación, Gaspar de Carvajal's Descubrimiento, Alvar Núñez Cabeza de Vaca's Naufragios... The feeling of wonder is all over the place, while the descriptions are rather correct in general terms. The Amazon river is so immense, that Gonzalo Fernández de Oviedo takes some time to give specifc news on natural phenomena that were unheard of in the Old World, and dedicates an entire chapter to that river. I will quote him on this passage, as he clearly states his sources (the translation is mine):

This mouth [of the Amazon river], that such a notorious thing God created in this World, was for a time called Sweet Sea, for with low sea sweet water gets into the sea, as many leagues from the land as I have mentioned, and many more if we believe Vicente Yáñez Pinzón, that was who discovered this river, and one of three brother captains who went with the first admiral of the Indies into these parts on the first journey to these Indies. And he was the first Spaniard to give news of this great river, and he saw it, and who I heard say that he had discovered it in the year fifteen hundred, and that he had taken sweet water on the sea thirty leagues far from the mouth of this river, and other particularities I shall tell on book twenty three.

This information is actually correct, as with low tide, the Amazon river gets into the sea, and thirty leagues (165 Km) from the sea you can get sweet water. Let's not fail to notice the language he uses, as he says "such a notorious thing that God created in this world". He also mentions that the width of the mouth of the river to be twenty leagues (some 110 Km), which as accurate, as the mouth of the Amazon river forms a delta the width of wich is some 100 kilometers and more. This is absolutely unfathomably large, as the mouths of the largest rivers in Europe known to Oviedo were along the lines of less than one mile (Guadalquivir, Scheldt).

Gaspar de Carvajal, who was the chronicler of Orellana's discovery of the Amazon river, also tries to be as objetive as he can, but cannot fail to use the syntagm "cosa maravillosa de ver" (admirable thing to behold) every so often, because he knows that this things are borderline otherworldly. Christopher Columbus himself, on his third voyage, was so completely stunned, and his knowledge of the World was so challenged, that he thought he had arrived to the very Earthly Paradise, the Garden of Eden, itself. He says the following (translation mine):

Great evidence is this that of the Earthly Paradise, for this place conforms to what those saints and holy theologians said, and furthermore are the signals very conform with this, that I had never read nor heard that so much sweet water could there be, inside and alongside salty water, and in that the moderate temperance also contributes, for I don't think a river this wide and deep is known in this world.

Hernán Cortés himself was also fascinated with what he saw, and that can be easily inferred from the frequency of the words "maravilla", "maravilloso", and "maravillosa" (wonder and wonderful), for the things he was seeing could hardly be believed. In his first Carta de Relación he could not fail to mention the Popocatépetl volcano, so large and impressive as it was. I translate again:

As I have always desired to give You Highness a very particular account of all the things of this lands, so I wanted to know the secret of this, as it appeared to me something wonderful, so I sent ten of my companions, of the type that was required for such an enterprise, and with some naturals of this lands to guide them, and instructed them to go up that range and know the secret of that smoke. They went there, and tried as much as possible to climb it, but they were not able to, because how much snow there is on that range, and the many whirlwinds of ash that from there come and roam the land, and for they were not able to suffer the great cold that there is up there, but they came very close to the summit, so much that while being there the smoke started to come out, and they said that I came out with such strength and noise that it would look like the whole range would go down, and so they came back down.

For any geographical accident, you will find Spanish witnesses admiring it and trying to give a detailed account, as it was necessary to have all the possible information in order to plan the provincial divisions, the adminstration, to know where people live, how many subjects there are, and all of the necessary information for an efficient administration. So, long story short, the Spanish colonists and conquistadors mostly reacted with absolute wonder and bewilderment at this new world's admirable geography.

Sources:

Fernández de Oviedo, Gonzalo (1535), Historia General y Natural de las Indias. Seville: Montesdoca. Modern edition by Juan Pérez de Tudela (1992, Madrid: BAE).

Cortés, Hernán (1519-26), Cartas de relación. Modern edition by Mario Hernández (1988, Madrid: Historia 16)

Colón, Cristóbal (1493-1505), Cartas y relaciones. Edition from Biblioteca Clásica, volume CLXIV, Madrid: Viuda de Hernando, 1892.

Carvajal, Gaspar de (ca. 1550), Relación del descubrimiento del famoso río grande, que desde su nacimiento hasta el mar descubrió el capitán Orellana. Manuscript in the Biblioteca Nacional de España, digitised here. Modern edition by Mariano Cuesta (1993, Madrid: RABM).

Myers, Kathleen Ann (2007), Fernández de Oviedo's chronicle of America: A New History for a New World. Austin: University of Texas Press.

Wayne, Franklin (1979), Discoverers, Explorers, Settlers: The Diligent Writers of Early America. Chicago: University Press.

I would like to add to u/TywinDeVillena's post from a different perspective. The German-speaking colonists/conquistadors/merchants that arrived in the Americas were often at odds with the New World. Their view of the Caribbean world, in particular, demonstrates that even as the Iberian settlers worked to make something out of the newness of the Caribbean, other cultures struggled using the same resources. In the 1550s, the Audiencia of Santo Domingo requested depositions from Venezuela's colonial population about some German-speaking miners who arrived under the Welser Company's experiment with the territory in the early 1530s. Of the nearly 50 who arrived in the New World, few Iberian colonists could think of a single one who survived the hardships of coastal colonial life in Venezuela's brief colonial capital, Coro. The few that had direct access to those peoples commented that the weather and the landscape was too much for the "Alemanes". I counted nearly a dozen in a single deposition from people that remained in Venezuela. They all mention the weather and the landscape, without explaining how Iberians were able to stand such climates alongside their Imperial cousins. I have been working to see what happened to those miners who happened to escape to other parts of the New World like Colombia, the Valley of Mexico, and the Yucatan, but the documentation is spotty at best.

We do, however, have their own words to describe the experiences of the German-speaking miners. While in the southern Caribbean, Titus Neukomm, a resident from Landau, testified to a translator that "here the land is quite hot and for our people, very unhealthy." [Que aqui todos soportamos una tierra muy caliente y para nuestra nación muy malsana...] One miner did survive the weather and tried to explain how so few of his fellow German-speakers survived. Urban Belem, a resident of Joachimsthal on the current Czech border, said the weather was the key issue. One German-speaker who died a terrible death in the Yucatan after fleeing the poor colony of Venezuela complained that the "tiger" attacks in the South American jungles were too much to bear. His brief letter to the crown made it seem that Germans in particular were bothered by the "tigers" whereas Iberians were not. Perhaps they were more concerned with the indigenous attacks, something that this particular German-speaker would die from in the later conflicts with the Maya. Philipp von Hutten, one of the more elite-born conquistadors from the Conquest period, wrote a series of letters from the wilds of Venezuela to his family in Europe. Before he died (beheaded by a political rival) he wrote that the land of Venezuela was difficult for everyone. He described a desert of jungle. Think about that. We do not usually refer to the dense jungles as a desert, but Von Hutten was attempting to explain to his brother in Europe the problems that settlement created for the conquistadors and merchants of the area. There was no food, no clean water that was plentiful and easy to find, wild animals, attacks from the indigenous nations, and even rebellion among the conquistadores themselves. Von Hutten even notes that life was preferable on campaign than back in camp: "We believed that in Coro, after our lengthy and tiring journey, we could relax and recuperate. Yet, we found a land so devastated that we suffered more than during the expedition."

I should say that the Iberians were not fans of the Venezuelan jungles either. The desert-like coast and the dense forests inland were brutal for settlers who first experienced the rather settled city of Santo Domingo before departing to the southern Caribbean. The few Europeans who attempted to conquer Venezuela and then traveled west into the comfortable and relatively peaceful highlands of Colombia's jungles rarely returned willingly to Venezuela or any other place again.

Friede, Los Welser

Avellaneda, Los Compañeros de Federmann

Von Hutten, Das Gold der Neuen Welt