White folks did enslave Native Americans across the Americas before the use of African slaves in the New World. This practice was most notably used by the Spanish in the encomienda system and later by the same with the repartimiento system. There were some differences between these systems and Atlantic slavery which was dominated by enslaved African labor, but the enslavement of Native Americans did in fact occur in both North and South America for centuries. That is sort of out of the scope of your question, but I'd love to discuss these differences in a separate question if you are interested.

As for why enslavement of Native Americans failed - there simply weren't that many Native Americans to enslave at the time of the explosion of slave labor. In 1492, there were millions of people living in the New World, but the arrival of Columbus and other conquistadors was catastrophic on local populations. Many of these folks died of disease - I probably am not the first person to tell you that 90% of some of these societies were wiped out by disease. This did not just include costal areas; there was a complicated system of trade, war, and interaction between native societies far predating Columbus's arrival. Those who survived the disease outbreaks were generally massacred en-masse: entire groups of people were wiped off the face of the planet. The survivors of both war/genocide and disease were few and far between, so large-scale slavery, particularly that of the early days - mining and other extremely dangerous and backbreaking work that predated plantation agriculture - just was too much. Many of these people were survivors of war and disease, so in some cases they could have been left disfigured or otherwise injured, meaning it was difficult to even find individuals "suitable" for bondage. Those who remained were enslaved oftentimes, but the rate of death in the New World colonies - especially at the time we're talking about - was incredibly high, so it was unlikely these folks would survive long. Populations did recover in some places and in others the Repartimiento system remained in effect until the 19th Century, and California in the USA is infamous for its enslavement of American Indian tribes.

Asian folks were far away and built complex societies which were perceived as harder to play off one another and were so far away that kidnapping or purchasing them was too much of a hassle to then bring them to the New World from Europe - you'd have to either round the Cape of Good Hope (that is, go around Africa and then either come back or sail to the Americas from there, and the Pacific is A LOT larger than the Atlantic) or go PAST the Americas and then come back (again, the Pacific is significantly larger than the Atlantic). Either way, it wasn't really economical to source enslaved people from Asia, and once they got there, many Europeans questioned whether or not it would be possible to source them without violence in the first place: lot of the actual kidnapping or capture of people sold into Atlantic slavery from Africa were captured by Africans from other tribes/villages/empires/polities, and there weren't as many empires in Asia; many of the Asian powers were large empires that ostensibly held control over large populations and areas.

For a little while, this issue was avoided by the use of indentured servitude, which in the most simplistic of terms was a form of debt bondage, wherein a white person could essentially use themselves as collateral for a debt and be held in bondage/servitude for a predetermined amount of time (usually seven years). This fell out of favor because Europeans generally believed that other white people had pesky rights which made it more difficult to hold complete power and influence over someone. Scholarship also suggests that white indentured servitude failed because color was a really easy way to tell if someone was enslaved - if you saw a Black person in the South in the early 17-mid 19th centuries, you could safely assume that person was enslaved, and if they were unaccompanied, they were a runaway. White people benefited from the ability to simply blend in.

All of these reasons made Africans the most convenient (at this point, I have to mention I hate using that sort of terminology, but that is the thought process of the people we're dealing with, and it would ahistorical to present it another way) population to enslave. Bishop Bartolomé de las Casas, a Spaniard, is remembered as the person who first suggested it to the King of Spain. He argued that enslavement of Native Americans was immoral because of the suffering it caused them and that Africans were a much better substitute (as an aside, he did later claim that slavery period was immoral, but that was after the King of Spain listened to him and opened up the Atlantic Slave Trade which we are most familiar with). Politically, Africa was fragmented; Africa had a lot of polities which vied for political power and were more than willing to trade with whites in exchange for slaves, there was a massive population of Africans which could be drawn from, and winds/currents favored travel from Africa to the New World.

Moral and religious justification for enslavement of Africans did come, but that generally came later (excluding de las Casas).

Sources:

Native Americans:

Written Out of History: Contemporary Native American Narratives of Enslavement by Max Carocci

La Florida: Five Hundred Years of Hispanic Presence by Jane Landers

Encomienda or Slavery? The Spanish Crown's Choice of Labor Organization in Sixteenth-Century Spanish America (Also a source on Africans)

Free State Slavery: Bound Indian Labor and Slave Trafficking in California's Sacramento Valley

Europeans:

The Half has Never Been Told by Edward Baptist (Also a source on Africans)

Migration and Human Capital: Self-Selection of Indentured Servants to the Americas by Ran Abramitzky and Fabio Braggion

Africans:

The Costs of Coercion: African Agency in the Pre-Modern Atlantic World by Stephen D. Behrendt, David Eltis, and David Richardson

Las Casas and the Birth of Race by Diego von Vacano

The Half has Never Been Told by Edward Baptist (Also a source on white indentured servitude)

Encomienda or Slavery? The Spanish Crown's Choice of Labor Organization in Sixteenth-Century Spanish America (Also a source on Native Americans)

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EDIT: Fixed an error regarding the wording of the population decline of Native American societies resulting from the Colombian Exchange.

Please check out this previous topic with answers by u/anthropology_nerd, u/arkh4ngelsk, and myself. Native Americans were enslaved in massive numbers. However, it was harder to enslave them on their native lands because they could more easily escape and lead slave revolts, so they were often exported from the British US mainland colonies to the Caribbean. Imported African slaves did not pose this problem (although escaped slaves did still sometimes join Native communities).