I have recently played some DM and some of the players on the server were bragging about how they were Silver 2 without playing a single game of competitive. Is this possible and if yes then how is it achieved?
You cannot rank up without playing competitive games, nor can you ever get a rank without playing a few competitive games.
From the CS:GO Blog:
Q. Where can I see my own Skill Group?
A. Once your Skill Group has settled and you have won 10 competitive matches, your Skill Group will be displayed on the main menu.