"Invaders led by the Spanish conquistador Hernán Cortés overthrew the Aztec Empire by force and captured Tenochtitlan in 1521, bringing an end to Mesoamerica's last great native civilization ... The Spaniards then murdered thousands of Aztec nobles during a ritual dance ceremony, and Montezuma died under uncertain circumstances while in custody... European diseases like smallpox, mumps and measles were also powerful weapons against the local population, who lacked immunity to them...By 1520, smallpox had reduced the population of Tenochtitlan by 40% in just one year." [1]

Maybe an oversimplification to assert "the Europeans didn't topple any empire in the Americas"?

[1] https://www.history.com/topics/ancient-americas/aztecs