Which single factor do you think was most important in making the Spanish so successful during the contact period?
I would argue that the most important single factor helping the Spanish was the fact that they brought with them diseases to which the natives of the Americas had no immunity. This was not the only important factor, but I would argue that it was the most important.
The diseases that the Spanish brought over devastated the native populations. Since they could spread from native to native, they could travel from places where the Spanish actually were and kill people who had yet to set eyes on a Spaniard. This was tremendously beneficial to the Spaniards because it destabilized and severely weakened the societies that might have resisted them. For example, diseases that the Spanish brought killed large numbers of Incas, including their emperor. They had then engaged in a struggle over who would be the next emperor. Right after that struggle ended, the Spanish came to conquer the Incas. The fact that so many of them had died of disease and that they had then fought a civil war made it much easier for the Spaniards to win.