Hmm, I may be improperly using the word "cause" here because of the connotation of the word causality. I see what you are saying, I probably am using "cause" & "produces" interchangeably.
Can I set up an an example for you to translate into how we arrive at knowledge?
Let's say we both stumble upon a giant multi-level sandcastle on the beach. For the sake of this thought experiment, assume we never saw the creation of this sandcastle, nor can we observe any other sandcastles like it being caused into existence (i.e. it was there long before we existed, and we'll never observe one being created again)
Me, in my irrational Christian ways would use faith to say "well, I've never come across one of these before, but I would posit an intelligent designer caused the existence of that sandcastle". You, with your rational and logical models of scientific inference, would take all sorts of measurements and gather the available present evidence and extrapolate that data deep into the past. Given the benefit of time, you would argue the complex movements of the ocean against the rocks and beach likely formed the sandcastle in a slow process over millions of years.
After all, the only present observable evidence we have is the ocean, the waves, the rocks, the sand (and all those intertwined processes), so it's clearly the only way we can arrive at a cause, right?
Why a sandcastle? By using a known designed object as a stand-in for objects whose design is under dispute, you're inadvertently begging the question[0].
Scientists didn't just decide to hate creation one day, making up evolution in response. They looked at everything they saw[1], then over centuries of discovery, found that simple creation didn't agree with the evidence. On a shorter time scale, the same process leads born creationists (like myself) to accept evolution on its merits.
Also, when evolutionary biologists refer to processes that occur over vast lengths of time, they aren't using time for its "wishy-washy benefit[s]", they're using time because time is what they observe in the form of sedimentary layers, isotopic decay, and genetic drift. Science is not like Doctor Who, in that "timey wimey" hand waving is discouraged.
After all, the only present observable evidence we have is the ocean, the waves, the rocks, the sand (and all those intertwined processes), so it's clearly the only way we can arrive at a cause, right?
Can you provide a specific instance where an interventionist/creationist model provides better agreement with the evidence?
[0] https://en.wikipedia.org/wiki/Begging_the_question
[1] By which I mean conducted experiments, made observations, and gathered evidence.
In this context you should also note that simply positing an intelligent designer does not actually gain you anything. Explanations can be recognized by their ability to predict future observations. Positing an intelligent designer does not allow you to make any predictions whatsoever. There is nothing necessarily fundamentally wrong with positing an intelligent designer - it's just not an explanation - so, if you want to have an explanation, you are still on square one. You essentially just have given the thing you lack knowledge about a name, namely "intelligent designer", but you haven't gained any knowledge about it.
As for your sand castle example: Well, I don't really have a clue how a geologist or an archeologist would go about that, but presumably one could try and determine the structure of the castle, such as the form of the grains, and how they stick together, and find other instances of similar structure to try and figure out what kinds of processes might be able to form such a structure? But as always: When in doubt, we simply don't know.
Also, I smell the Boeing from the junkyard argument for creationism. In case I am right there, you urgently should educate yourself about what natural selection is and in particular how natural selection is not random, and how evolution without natural selection would not work.
Events can be observed. Causation is not an event, its a relationship between events which cannot be observed, only inferred. Science is entirely about developing, testing, and refining rules for inferring things that are not observed from things that are observed.
> Even in the recent case of a broken window, only your neighbor who saw the event could have a decent level of confidence in what caused it.
I disagree. Its quite possible, in many cases, to observe how it broke, what other objects are in proximity to the broken glass, and other things that were going on in the area and have a "decent confidence" in how it was broken without observing the actual event of breaking.
> Millions of tests, models, and inferences would only produce an educated guess as to what happened
To the extent that this is true, causality is always an educated guess even when you observe the event directly, and the educated guess, with or without observation of the event, can have any arbitrary degree of certainty.
You seem to just be repeating the belief in the myth that causation is directly observable and that science is about reporting observed causation, and not developing predictive rules. That's just plain wrong.
Empirical observation -- which never includes causation -- is the input of science, but it is no the whole of the process. If it was, science would never get beyond describing events that occur (without their causes) and observed correlations. That's not what science is.