Hello
Is there any way to get permission to record the game?

Sorry for my bad english.

Hmm do I know you... unless Crytek lifts the NDA no. We can record the game just not upload it to public eyes, they recommend you record a bug or glitch so they can see it...

I know, but I would like to record these materials without incurring Crytek and would like to get a permit, the question is how to do it?

Bottom line is unfortunately you can't. Sorry!