It's by no means impossible, but don't expect absolute control
This is a picture of the British Empire, at its peak in 1921. At this point they controlled around one fifth of the total land area on Earth.
As you can see, the territories are spread far and wide, and so they didn't really have that much control. Eventually, control became influence.
However, it gets better
(Original source: https://www.essential-humanities.net/img/history/his46.jpg)
Behold the great Mongol Empire. At its greatest the Khans controlled most of central asia, and were only stopped by the Romans. They also had influence over India, but that's not shown on this map. Other than the Roman Empire, Mongolia controlled the entirety of (what was considered) the civilised world.
So it's not too unreasonable for an empire spanning the world, but it will split from internal pressures eventually, as at least someone is going to disagree.