No, that was absolutely not what happened. The discovery of radio waves happened in two parts: first, Maxwell completed the fundamental equations for electrodyn

No, that was absolutely not what happened. The discovery of radio waves happened in two parts: first, Maxwell completed the fundamental equations for electrodynamics by postulating that a temporally changing electrical field must be creating a magnetic field around it. Otherwise the behaviour of plate capacitors would be inconsistent. This brought the equations into a form that rather obviously allowed the derivation of a wave equation. Then it took about 20 years IIRC until Hertz managed to prove in his lab that these waves exist and can be both created and detected.