They had animals to pull carts: Dogs and humans. Plains groups had large breeds for travois pulling before horses were introduced. Dogs weren't used for physical labor in Mesoamerica, but they had large breeds like the loberro that were large and strong enough. Andean cultures had their own large breeds I'm less familiar with.
The plains example is particularly illustrative here though, because horses and knowledge of wheeled transports were introduced at roughly the same time, yet only horses were immediately adopted by nomadic plains groups and used to pull larger versions of the travois they had been pulling with dogs for centuries. The wheel just wasn't that useful because there was no road infrastructure to make it viable.
And so it was with virtually all of the Americas. Eurasian style road construction largely did not exist. The few places it did exist were enormously mountainous regions where a long distance journey was not reasonable by wheeled vehicle, and in those areas wheels remained relatively impractical for transportation purposes until the industrial invention of motors. Just to give some historical examples, the conditions in northern mexico were so rough that the most common kind of wagon often needed new axles daily. Spanish colonial authorities could afford nicer wagons and built them with all sorts of durability improvements like iron-banded wheels maintained on the journey by specialist carpenters, yet still regularly lost significant percentages of caravans to the conditions even on well-maintained trails like the camino real. Is it any wonder that people largely preferred to use mules or horses?
As an aside, wheelbarrows are much less useful without shovels. The primary digging implement in the Americas was a digging stick, the most basic versions of which are exactly what they sound like. Mesoamericans would occasionally have small wood or metal paddles at the end of theirs for various reasons. Descendants survive in modern tools like the coa used by jimadors to trim agave for tequila. For a large earthmoving project laborers would have used their digging sticks to loosen soil and hands or various small implements to scoop it into baskets or hides for transport by hand.
The plains example is particularly illustrative here though, because horses and knowledge of wheeled transports were introduced at roughly the same time, yet only horses were immediately adopted by nomadic plains groups and used to pull larger versions of the travois they had been pulling with dogs for centuries. The wheel just wasn't that useful because there was no road infrastructure to make it viable.
And so it was with virtually all of the Americas. Eurasian style road construction largely did not exist. The few places it did exist were enormously mountainous regions where a long distance journey was not reasonable by wheeled vehicle, and in those areas wheels remained relatively impractical for transportation purposes until the industrial invention of motors. Just to give some historical examples, the conditions in northern mexico were so rough that the most common kind of wagon often needed new axles daily. Spanish colonial authorities could afford nicer wagons and built them with all sorts of durability improvements like iron-banded wheels maintained on the journey by specialist carpenters, yet still regularly lost significant percentages of caravans to the conditions even on well-maintained trails like the camino real. Is it any wonder that people largely preferred to use mules or horses?
As an aside, wheelbarrows are much less useful without shovels. The primary digging implement in the Americas was a digging stick, the most basic versions of which are exactly what they sound like. Mesoamericans would occasionally have small wood or metal paddles at the end of theirs for various reasons. Descendants survive in modern tools like the coa used by jimadors to trim agave for tequila. For a large earthmoving project laborers would have used their digging sticks to loosen soil and hands or various small implements to scoop it into baskets or hides for transport by hand.