Monday
Monday, as a named concept, emerged approximately 2,000 years ago with the Roman adoption of the seven-day week. Prior civilisations organised time differently; the concept of a "first day of the work week" would have been incomprehensible to many ancient societies that operated on different calendrical systems.
Furthermore, Monday's continued existence depends entirely upon human civilisation maintaining its current temporal organisation. Should humanity adopt a different system - as has been proposed periodically throughout history - Monday would simply cease to exist as a meaningful concept.
The Moon
The Moon formed approximately 4.5 billion years ago, likely from debris ejected when a Mars-sized body collided with the early Earth. This makes the Moon roughly 2.25 billion times older than the concept of Monday. The Moon witnessed the emergence of life, the rise and fall of dinosaurs, and the entirety of human evolution.
Projections indicate the Moon will continue orbiting Earth for billions of years hence, gradually receding at a rate of 3.8 centimetres annually. Long after Monday has been forgotten - along with the civilisation that invented it - the Moon will remain.