I mean, European countries’ history is rich of thousands of years, whereas first European footsteps in America are 5 centuries old (I know there were natives before all that, but were they that many?).
Size mainly, they are huge countries with lots of cheap land and a historically (and deliberately) high immigration rate.
If you compare population density with those countries and European countries, you will notice that the US and Brazil density is still much lower than almost all European countries (especially their former colonisers), and the US, which is roughly the same size as Europe and Brazil which is 4/5 of Europe, still has less than half the population and a third the population of Europe respectively.
Also, progress in medicine and transportation means longer lives and ease of, well, just leave a crowded area and go somewhere else.
In theory, if the colonizers hadn’t arrived, the indigenous population could have reached the same numbers today. So, it has nothing to do with colonizers being outnumbered by the colonized. Just bigger country side in warm lands = more people.
Glad you said in warm lands. True that Canada and Russia didn’t reach the same amount of people even with their bigger size
Plus there were a lot of people on this side of the world, but they were decimated by diseases brought in from Europe.