Think of AD and BC dates as positive and negative numbers.

The Aztec Empire proper was around from 1428 to 1521 AD, that is, the years "+1428" to "+1521".

Ancient Egypt was around from about 3100 BC to, depending on exactly where you draw the line, 30 BC, that is, the years "-3100" to "-30".

Which is bigger? -3000 or +1428? Obviously, the positive one. The Aztecs came many, many centuries after the Egyptians.