I may miss the obvious solution (and maybe someone will propose Geometry Nodes?)
A method would consist on simply create a second sphere, that is slightly bigger than your globe, give it a material with your image on transparent background: Plug your Texture > Image Texture with your image into the Color input of the Principled BSDF and the Alpha into the Alpha. In Eevee in order to have transparency you need to go into the Material panel > Settings > Blend Mode > Alpha Blend, and Shadow Mode > None. Parent your globe to an empty and rotate with RR until it has the wanted position. You can create as many globes as you have continents. At the end you'll be able to bake onto a unique image texture if needed:


Former solution (Vklidu's): there's a problem with this method as the image will appear at the opposite side of the object, maybe there's an easy fix? Anyway, here is the material setup for the sphere:
- You need to create one Input > Texture Coordinate per continent, use their Object output, create as many empties as you have continents, select the empty at the bottom of the Texture Coordinate
- Put a Vector > Mapping behind the Texture Coordinate, you'll have to tweak the Location values to put the image as the same position as the empty
- Create your continent images (square images with transparent background), load them into some Image Texture nodes that you switch to Extend mode
- Mix these Image Texture into a Color > MixRGB / Mix mode, use the Alpha output of the Image Texture as factor of the MixRGB. Create as many MixRGBs as you'll have overlapping continents
- Give your empties a Shrinkwrap constraint with the sphere as Target so that they always stick to the sphere, activate the Align to Normal > Z option

Now when you move the empties, the continents will follow:

For additional continent, just add a new MixRGB node:

– NicNamSam Apr 25 '22 at 20:13My continent PNG is stretching and distorting, as well as mirroring itself at the equator. How do I prevent this?
How do I move it around like you do in the gif?
Can you show what the mix nodes would look like as I add more continents?