Important question: How to make a 3d Sphere material into a 2d spherical texture?

I created a noise map for a planet only using noise notes and color ramps - the result is a fancy planet:
planet
Now I want to convert it into a 2d spherical earth map:


Like that one (real earth map):

But how?

UV sphere or Ico Sphere ? Is that object created on Blender (meaning with the correct UVmap created) ?

Yes, all made inside Blender. UV sphere or ico sphere does not matter, a solution for one of the two is enough for me. Any solution?

Place an equirectangular camera in the center of the sphere and render out i.e a 2:1 aspect image of the emission channel.

Thank you!

The solution I had in mind was to bake the texture (which is why I’ve asked for the kind of sphere first).

Ok thanks. But I think CarlG’s solution is easier.

Type of sphere doesn’t really matter. Not unless you’re going to deform the sphere which I find unlikely for a planet. Once you have the texture file(s) created, you can map them onto anything “sphere like” using either environment texture, image texture using sphere/tube (depends?) mapping, or a custom node that redefines the generated/object mapping coordinates into spherical/cylindrical mapping.

If the texture is supposed to be locked to certain deformations, then I think I would unwrap. Generated mapping as a base may follow some type of deformations, but not others. Not sure which.