I'm 90% sure Player 388 is lying. Spoilers ahead.
I think he's either: Not a marine , or signed up for Marine, got the tattoo, then left.
My personal proof.
When asked his Class Number he hesitates and tries to laugh it off, only to genuinely overcompensate when 390 reveals his tattoo.
When asked about why his mom let him go he stays silent for like 3 full seconds and then says his dad made him go. I believe he came up with the lie about his dad (This could also be interpreted as him being ashamed or scared of his dad)
390 then asks about his Dad's time in Vietnam and 388 straight up ignores him and seems very uncomfortable and avoids the question by asking their names
The gun. The moment he holds the gun he legit has NO IDEA how to even hold it, bro has never held a gun before. If he had PTSD , if he was a soldier with trauma, he'd most likely still know how to hold it and reload it. Doesn't matter if the MP5 is not standard issue, its a gun. He should know the basics. He LOOKS AROUND to check how others are doing it. People say regression, but I still think that's far fetched.
Of course his whole episode 7 shooting and ammo thing. People say its PTSD but I think he's just a normal dude who got scared.
During episode 6 when Circle vs Crosses are arguing at around 41 minute mark, 388 gets pissed at the other side and tries to show himself as super macho by showing his tattoo and screaming "I'M A MARINE" ... this just screams playing too much into the lie.
It makes narrative sense. He lied about being a marine to 390. And now 390 is dead. This will probably BREAK 388 in the next season and he'll have to compensate somehow.
I like 388, I feel like his response in Episode 7 was a natural thing, but I do not think it was PTSD. I think we forget a lot of the players in the Squid Games, aside from being poor, are also not the best of people.