If this situation applies to you, I know how you feel. I know how frustrating it can be just to sit on the organ bench even without a single thought of how to start your improvisation.
It's amazing how simple it can be to improvise a theme on the organ. Yes, a theme is exactly what many of the good organ compositions have in the opening.
Let's establish for our purposes that a theme for improvisation is like a question. What you need to do next is to provide an answer to this question.
That's it, folks. It's that simple.
Of course, your improvisations can be very elaborate and can last a long time but the very first step you need to do is to improvise this answer.
So the question is a melody of about 4-6 measures long which may or may not end on the note of the tonic chord of the key (1st, 3rd, or 5th scale degree). It's better if this question ends on a different note than tonic because it propels the melody forward.
Usually it ends on the note of the dominant chord (5th, 7th, or 2nd scale degree). Although there are many paths you can take making your answer more interesting and advanced, the simplest form of it might be just to repeat the question and end it on the tonic.
Now when you know how to construct an answer from the question, you can harmonize it in four parts following the rules of harmony and voice-leading and you may just have enough of musical material for a short prelude or interlude in your church service.
By the way, do you want to learn my special powerful techniques which help me to master any piece of organ music up to 10 times faster? If so, download my video Organ Practice Guide.