Since department heads are in the line of succession, and

[haele]

4. I doubt it would be a cabinet position.

It's a vanity advisory department with a kewl name. I thought about it a bit, and remembered setting up a new government project of any type department isn't something that can be done in a couple weeks.
I doubt Congress will fund the implementation of a brand new department, even if they put it under GSA or some other actual Department.
*rump got lucky with Space Force, it was already a Command and the only money (granted, it was a lot of money) to be spent would be on the change in "the brand" - uniforms, stationary, logos, plaques, ect.
Musk's "DOGE" vanity think tank/advisory board would be at least quadruple the cost to wind up a department that would actually be able to implement changes. And it would still be 3 or 4 years before his office would be ready to do anything.

He's just getting an ego-boo advisory group. Whether or not they can actually implement anything is another story. He's going to have to spend most his own money to set it up and actually do anything within a year.

Haele