Can I, as a DM, create a new class entirely? If I can, how do I develop class features? [closed]

I believe my campaign needs a new class entirely. As in, you can choose from barbarian, rogue, new class name, etc. I looked at the DMG and it says literally nothing about creating a new class from scratch. So I want to know if it is possible to do so.

If it is, I also want to know how to develop class features, y’know, like the barbarian’s rage feature, but for a new class.

Also, does any class in 5e have a proficiency that you can’t choose, like: “Your proficiencies are this and one other of your choice”?