Survival Horror is often designed to begin "In Media Reis". Often the characters begin running for their lives, and then work backwards to find some safety so they have time to figure out why. In other cases, they don't even bother to ask - zombies want to eat you, what more reason do you need to shoot them? The unknown is a powerful tool for horror, and doesn't matter in an action fest.
There is a place for starting slow, however. A normal day or two of the character's lives can make the player's more attached to what what is otherwise a collection of numbers and dice rolls. Some challenges that are not life and death matters can get new comers familiar with the system. This is also a chance to earn some altruism points -which can make the characters more unique than the average starting numbers and allow for greater danger later because they're tougher than beginners.
Dead and Back's Unit "2552" setting has many different ways to slowly bring in characters. If you begin in the 1970s, perhaps all the players are new conscripts going through basic training. This introduces them to the background characters, life in the army, and the somewhat disturbing procedures of the chemical augmentation process (Don't worry - the heart stopping every now and then is perfectly normal! Just not this long usually.) In a post 90s game, it can begin with normal police investigation and help familiarize players with the setting. (Gun laws are very different from the US for one, so the acquisition of gear is not going to be quite the same.) This can be a time of investigation and simply learning that there was a unit 2552 a revelation and a lead in to the next part. Hematavores don't usually spread the sickness, so the world is less apocalypse, and more "Jason Vorhees goes to Moscow".