I am thinking of writing a short story which starts with a character narrating then ends up being narrated by an omniscient character. What are the best ways of making this transition? I can't think of any book that does it, let alone a short story. The logic gap would be such that it would create some discomfort to the reader.
You are correct to be wary of POV changes like you're describing. This is (generally speaking) an even a bigger concern for a short story, where you have less space to establish these things.
One approach might be to essentially split the difference and go with a limited third person POV. This would allow you be privy to all the character's thoughts, yet make it easier to describe the world around them.
But there is nothing inherently "wrong" with your original notion. The best way to find out is simply to try it and see. If your draft feels clumsy, you can always rewrite. Many times writers will discover the POV they've initially chosen might be less optimal to another once they start drafting.
If it helps, you can draw attention to the POV change in some way, e.g., a paragraph space with asterisks. I would also suggest making it clear right away that you've changed POV by referring to the main character in the third person as soon as possible.
POV characters are not required.
You can always tell your story from the perspective of an omniscient narrator/storyteller, and whenever necessary zoom into an internal (POV) dialogue/observation.
Btw... what do you mean by a omniscient character? do you mean a character in your story? or just the narrator (which is usually not considered a character)
In a novel you could make a Book One vs Book Two split. This is a stronger division than a chapter and is common in longer novels. I've seen plenty that change the POV this way. It's also used for generational changes. Though sometimes it's done without much change at all.
But you're writing a short story. Make your change after a small division such as a line of dots or pound signs across the page with line breaks after. Be sure to state the transition.
As George left the village in search of adventure, he set into motion events not only with his travels but also back at the village. His mother was so upset at his leaving that...
Another method would be for the narrator to address the reader. This would only work in certain stories.
Once George decided to rescue the knight, it was all he could think about. How to get past the dragon, how to scale the wall, how to exit the castle. Explaining himself was one task too many, so I will tell you the rest of this tale.
You need to change more than just the narrator
As I understand it based on your question and comments; you want a character to narrate in third person for 1/2-2/3 of the story, then switch to an older version of the same character to narrate the conclusion. This is feasible but needs to be done careful.
The first thing you will need is a clear segmentation between the two. This should be the biggest break in your story; Book One, Book Two as Cyn suggests is good for a novel, a page break or multiple line break may be enough for a short story. The important page is to make it clear that the context for narration has changed.
With the break established you need to provide the new context for the narration. Make the passage of time clear, maybe through a shift in tense or similar.
Another consideration is to link the new narrator to the old, use distinctive phrasing or narrative style to make it clear that we know this narrator.
It may a good idea to end the first part on a major story-shaping event. Something dramatic that it would make sense for the character to reflect on years later.
Jack pumped the brakes again, still no effect. The cliff edge was approaching faster now. He looked over to Jill and saw the terror in her eyes as the car plunged over the cliff.
When Jack looks back on that moment, he realises how lucky he was to survive the crash. Jill spent three months in hospital while he..... etc.