When were European settlers sure that the New World was suitable for habitation?

This may be a strange question coming from me, seeing as how I was born in the United States. However, sometimes I like to take a step back and look at the bigger picture. Historically, the residents of the Old World (specifically Europeans in this case) did not even know about the existence of the New World (let's just simplify it to the continent of North America in this case) until very recently. Leif Erikson may have reached Canada ca. 1000, and Christopher Columbus reached The Bahamas in 1492.

But at that time, it wouldn't have been immediately obvious that North America was actually viable for permanent habitation by Europeans. If I were living in Europe in the late 15th century, I could have believed that North America was like Mordor from The Lord of the Rings for all I knew. It's only by luck that North America has relatively similar climates and geography to Europe, but this wouldn't have been obvious after a quick glance at tiny portions of this continent's eastern coast.

When did European settlers finally realize that they could enjoy a high quality of life on this new continent pretty much indefinitely? For all they knew, North America could have been full of dangerous natural hazards like Mt. Vesuvius that destroyed Pompeii in 79 AD (like Mt. Saint Helens that erupted in 1980) or earthquakes like the one that destroyed Lisbon in 1755 (like the Good Friday one that hit Alaska in 1964). When did they understand that North America wasn't all fire and brimstone on earth where everything is trying to kill you?

There were many hostile Indigenous communities that attacked European settlers. There were many wild animals that killed European settlers. And as we know even today, cold winters and hot summers did kill many people. For all they know, they could have accidentally set off a booby trap or colonized a continent that was a ticking time bomb. They could have attempted to expand westward, reached the Appalachian Mountains, and given up at that point. They could have done the same after reaching the Rocky Mountains, but they didn't.

At what point did Americans reach the understanding that they had "gotten away with" settling in this continent? Even after the United States of America declared independence from Great Britain in 1776, there was no indication necessarily that the new country would be economically prosperous. The British could have taken America back in the War of 1812. The Wall Street crash of 1929 could have bankrupted the United States. The Axis powers (though unlikely) could have won WWII in 1945. But none of those things happened, and the United States in fact became the world's sole remaining superpower after the Soviet Union collapsed in 1991.

Of course today, we understand the United States of America to be the most powerful country in the world. But if I were a skeptical European living in 1492, I wouldn't even be sure that this new continent would be safe to set foot on. Only after many generations was it proven that the new continent wouldn't swallow people whole, or provide divine supernatural retribution for being unwelcome invaders. Now White Americans understand the geography of North America just as well as they do of Europe, but at which point historically did this become a certainty? When did they realize they were safe from harm and could develop permanent habitations in North America? When was it obvious to the world that the United States was in fact politically stable and not prone to collapse?