God did act on His desire. His requisite action was that He sent Jesus Christ, making it possible and available for all men to be saved.
If you think I'm missing the point, please explain how.
What do you think the answer to your question is?
For love to be love it requires an action. That's the point of the story of the good Samaritan. The one who loved his neighbour not only had compassion but acted on behalf of another. God also was compelled to act on behalf of the world if He loves the world. And so He has.
The impetus for the action isn't desire...it is love. John 3:16 doesn't say that God desired that all men be saved so He sent His Son. It says He loved so He sent His Son.
If you return to the OP the question never dealt with love...only desire. And the only question was whether or not a desire requires an action to be a desire.
While I do believe love requires God to act, I don't believe desire does.
People seem to conflate desire and love. I'm asking whether there is biblical evidence that desire requires action. It's readily available when it comes to love. I've yet to find it concerning desire.
Do you know of any verses or portions of scripture that make this clear?