I cannot tell you how so every single source of information from magazine articles to wikipedia and documentaries and fuck even fictional works such as Hollywood films and video games will ALWAYS mention the religious fanaticism of the Spaniards as they explored the new world.
As opposed to other European superpowers, GOD is JUST CONSIDERED equally important to the other two Gs according to most sources as to why the Spanish were so eager to explore the new world with some biased pro-Roman Catholic sources even stating it was the eagerness to spread the gospel that was actually even far more important to the Spanish enthusiasm than any money and prestige that Spain can earn from entering the new world.
On top of that I cannot tell you how many sources-not simply from the Spanish and Catholic Church but even OTHER Europeans observing the Spanish colonization of the Americas including mercenaries who fought alongside the Conquistadors (but only for Gold), other anti-Catholic nationalist politicians including monarchs of nations (too many to name), and even the defeated indigenous peoples the Spanish enslaved- would emphasize the RELIGIOUS BLOODTHIRST to spread the gospels and kill all who would refuse was ABSOLUTELY important for the Spanish success.
So many sources including anti-Spanish and anti-Catholic ones would describe the shock the Conquistador's enemies (including other European superpowers such as the French, Portuguese, and English) felt when they saw these soldiers of the Pope would not break down even in the most hopeless of situations and continue battling with an abnormal bloodlust. Indeed just the extent of how much Conquistadors prayed and brought religious elements (even bringing multiple heavy life real crosses that can be used to execute a live man) was incomprehensible even to other Catholic colonial powers and there are cases of Spanish generals even leading enthusiastic armies to proselytize other South American peoples and Indian tribes to the Roman faith even if there was no gold nor glory to attain.
Hell I seen a magazine years ago even state that without the religious fundamentalism Spanish culture had during this time none of the advantages they had in the new world such as superior weaponry, political alliances with natives, and disease wiping out entire populations, etc would have mattered. That the reason the Spanish were ultimately successful was because their belief in Jesus christ gave them an unyielding fortitude that allowed them to continue conquering when other European powers including Portugal would give up. (Though I must admit this article was admittedly Christian themed and was praising about how faith in Jesus Christ would enable miracles including articles on people with Cancer praying and miraculously getting cured).
However a lot of the sources i read were incredibly biased. Even the anti-Catholic sources that respected the Spaniards often used this holy war mindset that Spain supposedly possessed as another reason to demonize the Spanish. And I don't need to go into the details of how the Catholic Church profited so much from Spain's venture they granted her the title of "Bulwark of the Church" and wrote nothing but great things about the Conquista for the most part (well I know there are priests who oppose the Spanish abuses on local peoples and other stuff but thats another topic for another time).
So I am curious how different would the expeditions in the new world have been if the Spanish were primarily concern with practical matters and religious was merely an added reward along the way? Or at least, if the Conquistadors lacked the Jihadist religious fanaticism associated with Spain in this time period?
How would moderate or atheist anti-religion Conquistadors have done? Was this absolute conviction in believing Jesus Christ essential as many sources say? Or would Cortes and other explorers and conquerors still have the same success as OTL if say this alternate timeline has an irreligious Spain?