The very beginning of Jarhead is Jake at bootcamp (the DI with a little mustache is yelling at “the recruit” for not being able to draw), then I think it cuts to training (this transition seems sort of weak, I doubt they’d train him to be a sniper at bootcamp), then he goes to the Middle East.
No marine movie could be complete without a boot camp scene. Its the crucial part of a soldiers life. Its where they break him down, destroy what he was, make him a soldier. Why would you want a movie without a scene like that?
But to answer the question at hand,
Black Hawk Down is a good one that meets your criteria.
LOL . cause I seen enough of them , I get it. But sometimes i get the idea its part of the marine package that the corps gives to film makers , we can give ya 72 hours of an MEU , you just have to add the boot camp scene, so we can enlist some more boots.
I am not sure BHD was a marine movie though , seemed more army.
As well, hate to nitpick , but some of the leathernecks might get a bit upset being called soldiers, almost as bad as some of the navial aviators being called pilots.