How would I make this animation?

Greetings!!

How could I replicate this animation (the sphere intro part) in Blender? I would also like to use Cycles as the engine.

Looking forward to learning how to do this from your comments.

Is it even possible?

Of course it is.
I suggest you start experimenting with something like the screw modifier animating the angle value.
See attached blend for a demo of the animated angle effect

Attachments

screw.blend (92.7 KB)

Never even thought about the screw modifier… thanks for that. Looking at the blend now.