Instead he woke up but in his own subconscious - which is literally littered with pop culture references
In this case, it seems the best place to start is to ask some questions about your main character. What kind of references would he be familiar with? Movie quotes? Sports? History? Video games?
For example, take
Life is Strange. (spoilers for the first 2 minutes or so) The main character, Max was developed very carefully. She's shy and introverted, likes "nerdy" things, and dislikes the popular cliques. She's into photography, likes indie folk music, watches old movies, and gets along better with animals than with people.
What DONTNOD did here was create a very specific character that a very specific group of people will be able to relate to. Sure, they might have wound up driving away certain audiences with this approach. But ultimately, they struck a chord with their target audience instead of trying to create a "blank slate"-type character. Compare Max to Gordon Freeman from
Half-Life. Whether or not you personally are able to identify with Max, it's inarguable that she's a better developed character than the mute scientist-turned-superhero. Sure, I doubt many people were driven away from
Half-Life because they disagreed with the character of Gordon, but that's only because there's so little to disagree with!
So. I would first develop the main character. Then, once you have that solidified, you'll be able to better decide which references make sense within the context of the game. Bear in mind: the wider your target audience, the more of your references will go over any given player's head.
Disclaimer: I know very little about Half-Life 2, and from what I do know of it, that's where most of Gordon's character is developed. As a result, this example might not be wholly accurate; I was simply using him as an example of the "mute main character" archetype.