People in America were not stupid, there were not repetition guns yet, like Repeating rifle or early machine guns.
The biggest significant factor for Spanish people was getting the support of the local population. It was not foreign powers against local powers. But local powers against local powers.
And that was because local empires were terrible with the subdued tribes. There was human sacrifices with subdued tribes and they were slaves. Under Spanish rule those who supported the Spaniards were soon considered Spanish citizens, a huge improvement.
And Rome usually worked the other way around. Rome did outnumber everybody and squashed any opposition. First they did because mandatory Conscription ("the draft")in the army, an army of peasants that was way more numerous than anybody else and a population that will replace casualties much faster than anybody else.
The Army of peasants did fight against elite warriors that were much better trained and equipped but were way less numerous, for example against the Macedonian Army,and they won.
Finally, after growing and organizing themselves much more, Rome will use infrastructure that only they had like the Mediterranean sea and specially roads to move massive amounts of soldiers very fast from one part of the Empire to another.
This was the equivalent of the train that will make it possible for Germany, Russia or the US moving so much people to the war front fast.
It was the Romans those who did outnumber everybody else concentrating the army at one point, defeating the enemy and moving the Army to another place.
And it was Julius Caesar who wrote "divide et impera" because that was the Roman way of doing things, dividing their enemies, and fighting them isolated with a much bigger army.