The Finns always remained in Finland, even when they were under Russian occupation. Similarly when the Swedes owned the land the language never "died out" as such, as it was still spoken by the majority of people - Swedish became Finland's second language however, as the nobility spoke it.

On the other hand, the Americas saw huge swathes of native people dying due to disease and/or conquest, and colonialism took root. The modern nations are mostly based on the colonies that founded them, and so the languages spoken by the colonists have become the main ones, in almost all countries except Paraguay (where Guaraní is still the most spoken language).

The main difference is the fact that Finland was never a colonial nation, that is, it was always in Europe and therefore was never exposed to the difficulties nations that were not European (e.g. Native American peoples) had. Africa is an interesting thing to think about here - although it was colonised to a similar extent to the new world, the native languages remained. People did not die from diseases in the same way that they did across the Atlantic, as traders would already have brought the diseases millennia ago.

All American countries use languages which are not indigenous as the main languages

Slight nitpick: Guaraní is more widely spoken in Paraguay than Spanish (though both are spoken as a first or second language by >85% of the population), and both are official languages.