The fastest way is to boost kills Offline in Arms Race. You can get the 27 kills needed to finish the match in about 3-4 minutes while also going towards the 5,000 matches played in Arms Race/Demolition.
The reason why Arms Race is the easiest is because incase you die you respawn immediately so there is no wasted time in spectator mode.
Personally I like playing on Shoots, because it is a lot easier to maneuver than baggage.
Gametype: Arms Race
This should take around 20-30 hours depending on your skill.
If you have any other tips/tricks leave them in the comment section.
ALSO!! if you're going to give me a dislike please state WHY, so I can therefore fix whatever you don't agree with.
NOTE: If you go into an Arms Race game that is offline, choose your team and then switch team. Switch back again to the team you were in first and the game will be 5v5 instead of 4v4 :) makes it faster to finish.
Best Boosting strategy: (Thanks to IXI Falcon)
Get 10 people to fill up an Arms Race match. Doesn't have to be 10 human players, so break out those second consoles and dummy accounts if you got em.
When the match starts, call vote for "choose the next map" and choose Shoots. Once the vote passes, every game after this will be on Shoots and will bypass the loading screen and warmup time. This is almost twice as fast as letting the game switch between Shoots and Baggage over and over.
Now you just need at least 1 person to get the 27 kills and finish the match. This is also the fastest way to rack up kills towards God of War, so you shouldn't have an issue finding someone to get kills. You can even have 1 person from each team go at the same time if you want.