Nobody knew how penecilin worked when it was first discovered (we now know it inhibits the growth of the bacterial cell wall) but that did not stop people using it, to good effect. Similar for many other discoveries/inventions.
More generally: technology (engineering) delivers results. Understanding why it does so is not required, and often comes quite late.
If you want explanation, that's a role of science, though it's often preceded by a very long period of systematic observation.
One striking example is geology, which has existed since at least the 17th century, but which didn't formally adopt its central organising and explanatory principle, of plate tectonics, until 1965. Biology (evolution and DNA), physics (celestial mechanics, particle physics, reletivity, and quantum theory), and chemistry (periodic table and electron orbitals) also come to mind.
Thermodynamics arose out of work with steam engines, and eventually developed to the point that the theoretical understanding and equations began driving, rather than being driven by, engineering accomplishments. Electrical engineering is another example where modern developments required understanding of, and calculations based on, circuit and field theory, rather than just more lab experimentation. (I'm hazy on details here, though this is my general understanding.)
There are practices which existed for many thousands of years before a deep understanding was achieved: fermentation, fire, firing ceramics, glassmaking, smelting metals, and many agricultural practices. Doing and understanding are separate undertakings.
Chemistry has only lately really become tractable, now that we can simulate appreciable quantities of matter in a computer and our simulations have become accurate enough to for instance reliably predict how certain molecules will orient themselves spatially (including folding).
However, this blundering about approach only works if almost anything could have worked and so you just keep trying until you hit upon it.
You can discover that eating one of the dozen types of plants growing on the hillside nearby treats toothache without any overarching theory about how that could work, just try eating stuff and see what happens - but you aren't going to invent the LED lamp this way.
Example: When we put a cable on the bottom of the ocean these days it's optical fibre rather than electrical. But, even with optical fibre, even the best stuff we can make, this will need amplifying for long distances or it's pretty awful. One thing you could do would be to choose reconstructing amplifiers when making the cable. So e.g. you decide this cable is Protocol X at 100Gb/s, you make amplifiers which can reconstruct a Protocol X signal at 100Gb/s and "boost" it, splice those in along the distance of the cable, and drop the whole lot into the ocean. However, somebody is going to invent 500Gb/s Protocol X+ and if you want to upgrade you will need to send teams down to the ocean floor to replace those amplifiers. Ouch.
In principle individual photons are travelling along the fibre, and physics doesn't say we can't just have one photon in => two photons out to boost this without needing to reconstruct the signal at all. There should be some way to build a device which does this, an Optical Amplifier, and it would be OK if this is quite expensive since it's saving you that enormous expense by allowing you to upgrade to 500 Gb/s X+ or to 10Tb/s XXX or whatever other future protocols just involve sending photons down a fibre without trying to upgrade equipment at the bottom of the ocean. But... how?
Turns out scientists can guess exactly how that should work if it's possible, and then direct the experiments, trying out only the handful of things which actually might work instead of just groping about at random. My alma mater was one of the places figuring out how to do this in the 1980s, they were still really proud of that when I studied there a decade later. Erbium Doped Fibre Amplifiers are the result.
I think that your fundamental premise is wrong: there've been a large number of ancient / preindustrial inventions which were not obvious, which were terrifically surprising, or which required a tremendous amount of skill or craft to accomplish. It'd be interesting to come up with a catalogue of these....
Your transoceanic cable example is an interesting one, as the first electrical / telegraph cables greatly expanded the understanding of electric fields and interactions with the environment, especially in salt-water.
I'm also wondering if there's some sort of frontier between the "just blundering around" approach --- mass parallel experimentation --- and "requires a substantive theoretical understanding". To take your LED example, LEDs are the inverse of the photoelectric effect (and apparent PV panels will emit photons when a charge is applied to them). Electroluminescence dates to 1907, whilst the first LEDs were developed in the 1960s. There were earlier similar phenomena such as chemoluminescence (including numerous examples of bioluminescence) which might have suggested the possibility.
I'm agreeing in part, disagreeing in part, and wondering if there might be a more robust or systematic way of distinguishing limits of both methods.
Sometimes it's surprising what nobody was interested in inventing. I think Grace Hopper is really important because people were resistant to the idea that programming the computer involved boring mindless steps which could be done by a machine and so of course instead of hand writing the program in machine code you should write a higher level language and have the machine translate that. It's incredible now, but this very idea was once an important invention and yet her superiors were not enthusiastic.
I'd heard of it via Isaac Asimov who mentions it in his biography and a few other contexts. Asimov was Stern's research assistant, and incorporated the ideas into several of his own stories.
It's not that simple. Lots of things that are discovered are discovered when the goal was something else entirely. The number of accidental inventions is very large and it isn't rare at all that the accidental invention (or, more appropriately named, accidental discovery) is of much more value to society than the original goal was.
Also, a lot of empirical progress in ML didn't happen until people stopped worrying about explainability and theoretical guarantees. Remember when NNs were unfashionable?
