Question

When was the atmosphere of the Earth formed?

Answer 1

The "Atmosphere" was present shortly after earth's formation - 5 billion years ago. Our current, human-compatible atmosphere developed over time, assuming its current composition only around 500 million years ago.
http://teachertech.rice.edu/Participants/louviere/history.html

https://scijinks.gov/atmosphere-formation/

GREAT Timeline graphic here!:
http://www.scientificpsychic.com/etc/timeline/atmosphere-composition.html

http://www.amnh.org/learn/pd/earth/pdf/evolution_earth_atmosphere.pdf