When I attended a Mind, Brain, and Learning conference a few years ago, a lecturer posed the following question (paraphrased):
If I ask you to figure out the cube root of a number like 150 in your head, and ask Albert Einstein or Richard Feynman to do the same, they will probably come up with the answer faster than you do. But who will be using more of their brain to do it? You or the great physicists of the era?
The answer, he went on to explain, was that you would be using more of your brain to do it. He went on to explain that experts use surprisingly small numbers of neurons to accomplish tasks within their own field of expertise. Experts have invested a great deal of time and calories into streamlining those systems, and making them extremely efficient.
Novices, by contrast, engage relatively vast swaths of their brains in order to accomplish tasks.
The streamlining that the experts have done is mastering abstractions.
To my way of thinking, your stated goal sounds very nice, but it doesn't really work.
The problem is that we naturally move from concrete to abstract, which is done in three parts: (1) we learn how something works, (2) we make the observation that "this is kind of like that" and then (3) we continue with the questions, "what other things are like these things? What are the common features in how they behave or function?"
Within the brain, it is actually the same three part process: (1) understand a system, (2) use the common parts of two systems to create a streamlined version of their common, essential parts, and then (3) connect that streamlined system to many other ideas.
(Please note the order in which I created that abstraction for you in the previous two paragraphs, and consider whether it would have been somehow clearer if I reversed them.)
The second and third phases are actually cyclical. When we connect to a new system (phase 3), we frequently wind up revisiting the second phase as the new, connecting ideas provide insight into the abstraction that we didn't notice before. Also notice that the order remains concrete to abstract even here, when we already have a good, abstract construction.
When we do all this, we are building our abstraction, which can also be described as winnowing down a system to its essential features. This process is insanely useful! (More on that in a bit.)
We don't work from abstract to concrete naturally, unless we already have good, firm ideas of the particular abstract systems being used.
If you want to get a sense of how hard this is for humans, notice how we struggle to explain the process of quantum computing, which puts us all in a position of having to begin abstractly, and attempting to concretize from there. It's so hard for precisely this reason. Without concrete systems that behave like the quantum systems, it is almost impossibly difficult for us to build up useful abstractions in the first place.
Why we frequently want to teach this way
You're not at all alone in wishing to teach the abstractions from the outset. (It is a bit of a perennial issue here on CSEducators, actually.) Teachers often really want to begin from the abstraction. It's instinctive!
After all, a firm abstraction is absolutely wonderful. It is a little key that opens vast swaths of thought to the key holder.
The abstraction is also much simpler than any of the derived systems, which have little details that can be hard to understand without thoroughly understanding the abstraction that makes the whole system work in the first place.
Once you have the abstraction in place, all of those confusing little details hardly need to be remembered. They can be quickly and trivially re-derived when we need them.
It makes sense that, almost as soon as we learn a good abstraction, we switch over to using it very heavily in our thinking. It vastly simplifies and streamlines our thought process when faced with complex systems. Win-win!
It is natural to want to get your students to think this way as well. After all, if they can see the bigger picture the way that you do, they will be able to take advantage of how simple it all is, just like you do. Why not start there, show them the beautiful simplicity, and then show them how trivial it is to now understand a lot of wonderful things?
Hopefully you can see the answer: the students can't do it. That mode of thinking is unlocked only by having at least one, and hopefully more, concrete, well-understood examples first, because those concrete examples are what permit us to comprehend the key secondary features.
Looking at it from a neural basis, the novice mind lacks the information that must be winnowed and simplified in order to create the streamlined pathways.
We teachers can absolutely help guide students along the path to these kinds of abstractions. But the first step to make it manageable for a human brain is to make sure that brain has a few concrete examples to work off of.
What we can really do
So how can you help your students get to the abstract part? You (1) journey through a topic concretely. You (2 and 3) regularly point out when something they're learning is similar to something they've already learned. You regularly discuss the abstract elements that are coming up.
Start concrete, move slowly towards the abstract.
It feels positively glacial to work this way, but that's partly an illusion. We simply forget how long it took us to find, winnow down, and make our own beautiful abstractions. The slow pace is really just the time it takes to build the abstraction in the students mind.