What is the source of all electromagnetic waves?

Accelerating charges.

Explanation:

Electromagnetic waves are waves produced by the vibration of both electrical and magnetic fields.

This interaction produces an energy source that does not require any medium to propagate.

To produce electromagnetic waves, electric and magnetic fields must be vibrating.

An electric charge produced when vibrating under voltage will produce electromagnetic waves. This is the same for all sources of these waves.

The sun produces electromagnetic waves. A lot of human activities also does this.