This page of the Call of Duty Cold War guide contains information on whether you will be able to finish the game quickly. Here you will find out how long it takes to complete the campaign, with and without searching for all kinds of secrets, and how much time you will need to complete 100% of the game.
If you want to play exclusively single player campaign, it will take you about 4-6 hours to complete it. If you want to find all the secrets and easter eggs during the campaign, it can take you up to 8 hours. It can take up to 12 hours to complete 100% of the game, including secrets and challenges. During a second and third playthrough, you will probably have to repeat some missions. To complete some of the game challenges, you will also have to play the outbreak and multiplayer modes.
It is worth mentioning that the game features certain choices that affect the ending of the game. The Mind Trip challenge itself requires the player to go through 4 final scenarios of the Break on Through mission and watch all 7 memories endings.
See Achievements for more information on challenges.