Sorry for responding to this so late, my IFTTT alert system seems to be broken.

The belief that nobody in the Americas had metal tools is incorrect. North Americans in particular had a long history of utilizing copper, notably the so called Old Copper Complex dates to several thousand years BC, but since you specifically asked about the Aztecs, Inca, and Maya, I’ll answer for them. I’m going to focus on the Aztecs and Maya because I specialize in Mesoamerica, but I will attempt to answer for the Andes as well.

Metallurgy is generally believed to have entered Mesoamerica between 650-800 AD via a maritime trade route connecting West Mexico to Ecuador^1 . The technology would have been transmitted by traders making long distance trips via balsa raft, and landing in West Mexican ports. The traders were probably seeking the spondylus oyster, which grew along the coast of West Mexico, and possessed a shell that was sacred to central and southern Andean peoples.

Early metallurgy in Mesoamerica, which was mostly confined to West Mexico, mainly utilized the techniques of wax casting and cold working and was used to make status items like lip plugs and bells (which were decorative items worn in wristbands, ankles, or sewn into clothing) as well as certain small tools like tweezers and needles. The primary metal used was copper.

By the Late Postclassic period (the exact definitions the temporal range of this period differ, but it usually means ~1300-1519 AD, and was notable for seeing the rise of the Tarascan Kingdom in West Mexico starting around 1350-1400 AD and the rise of the Aztec Empire starting around 1428 AD) in Mesoamerica, metallurgy had expanded in both area and the types of metals used, having become nearly ubiquitous throughout Mesoamerica. The smiths of West Mexico were still the most prominent metallurgists, using a variety of alloys such as copper-silver, copper-arsenic-tin, and two types of bronzes, copper-tin and copper-arsenic^2 . Arsenic bronze (copper-arsenic) was the most common of the two types of bronzes used, because tin was extremely scarce, with the only major source of tin near Mesoamerica located in the modern day state of Zacatecas, which is not technically even in Mesoamerica. Copper-tin, the rarer kind, is the type of bronze us westerners are most familiar with.

Metal was now also prevalent outside West Mexico, and the smiths at the Great Market of Tlatelolco, a famously large market on the same island as the Aztec capital of Tenochtitlan, are described as casting copper into bells, needles, axes, and awls^3 . It should be noted that Mesoamericans never adopted metal weapons on any large scale. This could be because it was considered an expensive and sacred material in some areas, and/or because copper and bronze could not be sharpened enough to match the effectiveness of the much more widely utilized obsidian, especially against Mesoamerican armor, which usually consisted of extremely thick jackets (one and a half to two fingers thick!) made of tightly woven cotton sewn onto a leather backing.

As for the Andes, the people there had a much longer metallurgical tradition than Mesoamerica. I’m less familiar with them, but according to The Ancient Central Andes by Jeffrey Quilter metal tools were in wide use by at least 1000 BC. Tools used included things like pins, needles, knives, axes, crowbars, and spear heads.

Back to Mesoamerica, it should be noted that Mesoamericans were able to accomplish some extremely impressive architectural feats with no metal tools whatsoever. The great city of Teotihuacan (100 BC-650 AD) and the massive pyramids there, as well as the even larger pyramids at El Mirador (~400 BC-150 BC), both predate metal tools, and the classical Maya civilization, the most famous phase of Maya history, involved no metal tools whatsoever. I am most familiar with Teotihuacan so I can shed some light on how Teotihuacanos built the enormous pyramids and temples that they did.

The largest pyramid in Teotihuacan, the Sun Pyramid, is about 63 meters (206 feet) tall and 216 meters (708 feet) wide. It has a volume of about 1,175,000 cubic meters^4 . Basically, the way they built it was by using what might seem like an absurd amount of human labor - the Pyramid of Sun is estimated to have required 12 million person days to complete. This is less than it seems, however - given 50 years for construction, the per capita burden for building the Pyramid would have only required each able bodied adult male in the city to spend 15 days a year constructing the pyramid. Additionally, in most cases, Mesoamerican pyramids were not built with large stone blocks but rather with small stone bricks, and then covered in a type of concrete or plaster. Further spreading out the burden, pyramids were often built in stages, starting small, and then progressively expanded over time. One layer would be built, and then “fill” of dirt, stone, and some other potential materials would be added in between the old pyramid and the new exterior of stone bricks. This was not always the case though, for example, the Temple of the Feathered Serpent at Teotihuacan is constructed of stone blocks weighing several hundred kilograms that were roughly cut and shaped at quarries several miles from the city, and then dragged by humans to the city and moved into place where they would be worked into their final forms.

Jewelry made of metal appeared in Mesoamerica after the advent of metalworking. Other materials like jade and various other precious stones were worked with the same tools used to make large and small sculpture - saws, blades, chisels, wedges, hammers, drills, and abrasives^3 .

SOURCES

1 Ancient West Mexican Metallurgy: South and Central American Origins and West Mexican Transformations by Dorothy Hosler

2 West Mexican Metallurgy: Revisited and Revised by Dorothy Hosler

3 Aztec Archaeology and Enthnohistory by Frances Berdan

4 Ancient Teotihuacan: Early Urbanism in Central Mexico by George Cowgill